It was the day before Sergey Brin's 30th birthday, and by all rights he should have been on top of the world. Here onstage in front of some 300 peers—engineers and other geeks attending a conference on Internet search—he was answering softball questions about Google, the search-engine company he co-founded five years ago. Brin likes to do this, and who can blame him? Google is among the most successful Silicon Valley startups of all time, and wherever Brin goes these days, he gets treated like a celebrity. "How did Google become such an icon?" the moderator asked. And, "Will you acquire Microsoft?"

But this time Brin wasn't reveling in it; he responded more like a rock star being asked to play his greatest hit one ... more ... time. Asked about consolidation in the search business, he said, "I preferred things during the bubble"—when Google was not so famous—"and we could go on doing our own thing." At the end of his presentation he repeated the thought, saying that coping with Google's torrid growth had become the worst part of his job: "It's a distraction from pure technology, which is what I love."

When Google goes public, most likely by this spring, Brin will become a billionaire. Make that a multibillionaire. So to hear him pining for the good old days sounds strange—especially since, thanks in part to Google, the Internet has never been more useful or fun than it is right now. Google's search service has changed the way everyone from CEOs to their teenagers look for and think about information, dominating search not just from its own site but also as the engine for major sites like Yahoo, AOL, and Amazon. Plus Google has triumphed in more than search; in the past two years it has astonished the online world by proving that Internet advertising really works. And in what may be the ultimate sign of success, Google has even become a verb, as in "I'm googling for the numbers now."

When the numbers pertain to Google, they look very, very good. In 18 months the company has quadrupled in size, now employing more than 1,300 people. Annualized revenues have sextupled, to about $900 million. Annualized pretax profits have grown by a factor of 23, to about $350 million, according to a handful of people who have been told the figures. Only a few high-tech companies in history, like Apple, Compaq, Sun, and more recently Amazon.com, have generated that kind of revenue growth so fast. None has made as much money doing it—not even Netscape, which grew faster than Google has but made money in only one of its years.

In fact, the only question about Google's future that people seem to debate is when, not if, the IPO will come. Barring any last-minute exception, by April 30 the company will be required to start publishing its financials—an SEC rule for firms with as many shareholders or option holders as Google has. So, the thinking goes, why not make a virtue of that loss of secrecy by raising buckets and buckets of cash?—as much as $2 billion, as analysts currently predict. A Google IPO of that size would be the largest by any startup in high-tech history and would probably value the company at about $20 billion, just a couple billion dollars north of what Google valued itself for when it proposed using stock to acquire social-networking site Friendster last summer.

As a soon-to-be billion-dollar baby, Brin ought to be in his glory. So why the dourness on stage? Over the course of four months FORTUNE has peered behind the curtain at Google, conducting more than two dozen interviews with employees, friends of employees, investors, business partners, and people exploring employment or business deals with the company. We talked to another dozen veterans of the search, online-advertising, and computer businesses. And we talked to the Google brain trust: Brin, co-founder Larry Page, CEO Eric Schmidt, and top exec Omid Kordistani. The reporting revealed plenty about a company that has succeeded on the Net beyond anyone's imagination. But it also turned up signs of trouble—enough to worry any founder and raise alarms for investors considering (and who isn't?) betting on the IPO.

We'll sing more of Google's praises later, but first the worrisome news: Google has grown arrogant, making some of its executives as frustrating to deal with in negotiations as AOL's cowboy salesmen during the bubble. It has grown so fast that employees and business partners are often confused about who does what. A rise of stock- and option-stoked greed is creating rifts within the company. Employees carp that Google is morphing in strange and nerve-racking ways. And talk swirls over the question of who's really in charge: CEO Schmidt or co-founders Brin and Page?

Such travails are hardly surprising in a startup that has grown so big and so fast. But now is a particularly unfortunate time for Google to be facing them. Competitors—the biggest and most powerful on the Net—are coming on strong. Microsoft is spending billions to build its own search engine that will be incorporated in both its online service MSN and its new operating system, due in 2006. That could push Google off tens of millions of PCs. Yahoo in the past year has methodically acquired the other top search engine companies—Inktomi and Overture Services—and is believed to be weeks away from ending its long partnership with Google so that it can compete head-to-head. Other heavyweights—AOL, eBay, and Amazon—are also drawing battle plans. All are aiming for what they see as Google's weak spot: lack of customer lock-in. Though its search engine is a wonderful tool for using the Net, what happens when a better search engine comes along? Or just a good-enough search engine in the hands of a powerful rival? Is there anything to keep users wedded to Google? "Google has a lot of momentum, but its current position is probably not defensible," says an investor.

Google's foes have a much firmer hold on customers, argues Seth Godin, a well-known Internet consultant and editor of last summer's widely distributed online book What Should Google Do? Competitors have troves of personal information about users that they draw on to customize products, ads, and services—consider the way My Yahoo brings you information on everything from your portfolio to fixing your house. They will probably use that same information to tailor search results. Google, meanwhile, knows little more about you than what you are currently searching for.

Page says he doesn't spend much time worrying about competitors: "That's not what we're about. We think of what we do as adding more value to the world." Yet investors—stockholders and the limited partners in Google-invested venture capital funds—are growing nervous. And no wonder. Members of those groups count as insiders who by standard IPO procedures will probably be required to wait at least six months before cashing out. Google may well be worth $20 billion when it goes public; but it could be worth much less by the time they can sell.

For Google's millions of users worldwide, and especially for its fans in Silicon Valley, the fact that anything could be seriously wrong there must strain credulity. In a short time Google has become one of the world's best-loved brands. Movie stars like Gwyneth Paltrow and ex-Presidents like Jimmy Carter drop by for visits. A thousand people apply for jobs at Google every day.

All this from a couple of eager grad students. The founding of Google is already the stuff of Silicon Valley legend. In 1995, Page and Brin were roller-hockey-obsessed doctoral students in computer science at Stanford. Brin was the talker of the two—originally from Moscow, he trained on the trapeze and seriously considered joining the circus. He and Page, a Michigan native, teamed to write a paper on crafting a better search engine. In the course of three years, they maxed out their credit cards building a prototype. Most search engines at the time based their results on how often a certain word appeared in any website; Brin and Page figured that more important was the relevance of a site and how many other web pages linked to it.

According to their algorithms, popularity mattered—and soon Brin and Page gained it for themselves. Though web-search startups were a dime a dozen, investors couldn't hand money over to Google fast enough. When the founders showed Sun Microsystems co-founder Andy Bechtolsheim a demo in the summer of 1998, he wrote a $100,000 check on the spot. Brin and Page had to wait a month until Google actually existed to cash it. In 1999 top venture capitalists Kleiner Perkins and Sequoia Capital invested $25 million. "It was very unfashionable to invest in a company like Google back then," said Michael Moritz, the Sequoia partner in charge of the deal, in an interview with FORTUNE last year. "But we thought Larry and Sergey were taking a fresh look." Soon after, Yahoo anted up $10 million.

Google was becoming a household word, serving up an estimated 60 million searches a day. But it still had no real way to make money. Revenues dribbled in, mostly from licensing the search service to other sites. For more than a year, the board pressed Brin and Page to get professional help, and in early 2001 they recruited Eric Schmidt. The fit looked perfect: He had deep technical roots (a Ph.D. in computer science and a run as CTO of Sun) and leadership experience too—he had just spent four years as CEO of networking pioneer Novell.

Most important was that even though Schmidt, now 48, was almost old enough to be Brin's or Page's father, he wasn't interested in pushing them aside, or in replacing the culture they had created. From the beginning, Brin and Page had envisioned building a company unlike most startups—an island of idealism where being too concerned with money or power would give you warts. "In the early days Larry and Sergey spent more time talking about how they weren't going to make money—no user registration, no blast e-mails, no banner advertising—than how they were," says a participant in Google's early discussions. On Google's website, under the heading "Ten things Google has found to be true," No. 6 still reads, "You can make money without doing evil." Not doing evil is a common concern around Google and loosely translates into avoiding anything that mars Google's user experience, "even at the expense of revenue," says Cindy McCaffrey, Google's marketing chief and an early employee.

All this was a little weird at first, Schmidt admits. He was startled to discover that the founders tell the staff every Friday how Google is doing, including an occasional detailed financial review. "I said, 'You can't do that,' " Schmidt recalled in an interview last year. But he realized that the meetings were ingrained in Google's culture and united the staff, so he relented.

Schmidt focused instead on transforming Google into a self-sustaining affair. Shortly after he arrived, he and the top execs got much more aggressive about generating revenue. They came up with a product, now known as Adwords, that allows users' search terms to trigger relevant text ads that appear onscreen to the right of the search results. It was similar to what another startup, Overture Services, was offering. Advertisers pay Google based on how many people click through to their site, allowing them to track effectiveness easily.

Unveiled in February 2002, Adwords now has more than 150,000 advertisers, many of whom rave about the service. Seth Berkowitz, the head of business development at Edmunds.com, an online car shopping site, says the response rate for his ads on Google has been so good that he has gone from buying $70,000 a month in advertising to $250,000 a month in less than a year. "It's the cheapest and most effective form of advertising ever created," Berkowitz says. He figures that every dollar spent with Google generates about $1.70 back.

This year Google came up with Adsense, which puts ads on nonsearch sites. Read about the New York marathon on newyorktimes.com, for instance, and Adsense serves up ads for sports drinks, running shoes, or whoever else pays. The ad businesses supercharged Google's growth. Yet through it all, the company hewed to Brin and Page's wacky vision, so that today Google seems firmly ambered in the dot-com era. At its Mountain View, Calif., headquarters, Google serves free lunch and dinner, prepared by the former chef of the Grateful Dead. It has an on-site masseuse. It takes the staff to Lake Tahoe for the weekend once a year. Dogs are welcome. The lobby and the office Brin and Page share are decorated with bean-bag chairs and lava lamps. And the organization remains almost entirely bureaucracy-free, a way of encouraging engineers to run with good ideas as they hatch them. Brin points to an example: Google News, which puts an astonishingly rich, up-to-the-minute compilation of the world's headlines at the user's fingertips, grew out of an engineer's self-directed project.

Sounds great! Well, maybe not. Those close to Google say that the company has begun to more closely resemble a madhouse than any kind of serene dot-com dream. It's a tough place to work, and a tough place to do business with.

Beyond the bean-bagged lobby, 12-hour days are considered standard, and an unspoken caste system has emerged. At the top are the engineers, people in the mold of Brin and Page. At the bottom are the contractors, the 30% of Google workers who labor alongside full-timers—yet without benefits, stock options, or access to the company intranet, not to mention to meetings or social events. That's fostered anger in Google's overeducated ranks. For the most part, it takes a degree from an Ivy League school, or MIT, Stanford, CalTech, or Carnegie Mellon—America's top engineering schools—even to get invited to interview. Brin and Page still keep a hand in all the hiring, from executives to administrative assistants. And to them, work experience counts far less than where you went to school, how you did on your SATs, and your grade-point average. "If you've been at Cisco for 20 years, they don't want you," says an employee.

Brin, Page, and Schmidt won't discuss specifics but agree that Google often values brainpower over experience. "Larry and Sergey have been far more disciplined about hiring than anyone I've ever met," Schmidt says. "The result has been that they have a company where fewer people can do a lot more."

Aversion to bureaucracy is turning out to be better in theory than in practice. People who work at or do business with Google worry that the company has outgrown that style. Ed Gilles, the CFO at storage software company Veritas, was in the running to become CFO at Google last year; he bowed out because he found the place too chaotic. (Onetime Sun CFO George Reyes now holds the job.) And in October, Sun co-founder Bill Joy and former Sun technology executive Mike Clary—both of whom know Schmidt from his days at Sun—kicked the tires at Google, only to walk away, telling others they were bewildered by how out-of-control things seemed. Gilles and Clary won't comment on their negotiations. Joy will say only that he talked to Google about working there and that the talks never reached a conclusion.

Business partners, meanwhile, have had trouble determining who makes decisions among Google's employees. A CEO who is negotiating a contract with Google and who asked to remain anonymous described a Dilbert-esque series of meetings: "Typically half the people show up 20 minutes late, so you have to repeat your presentation; another couple leave ten minutes early. Most of the time they're not paying attention anyway, but messaging each other and their friends on BlackBerrys and Danger hiptop machines." He says Google has hired so many people in its middle ranks and given so many the same title—project manager—that "no one can figure out who's in charge or even what Google's licensing policy is." People inside Google say the experience is far from unusual. "My take is that they are crumbling under the weight of their own success a bit," the CEO says.

The founders acknowledge that their company is more disorganized than most, though they say it's not arrogant. "We had to deal with arrogant dot-coms during the bubble, so it's something we take very seriously," says Brin. If people aren't prepared in meetings, he says, it's not because they think they're too good for them, but because they're working around the clock. Brin and Page mandate that employees spend 20% of their time on self-directed projects and another 20% interviewing outside job candidates. Getting ready for meetings (or showing up on time) doesn't always take priority. "It's a penalty we pay for making that deliberate choice," says Brin.

Okay, but where's Schmidt in all this? As the imported grownup, he was brought in to be a steadying hand. Yet people like Clary have lobbed charges that control rests too heavily with the founders and that Schmidt is just a figurehead. Friends of Schmidt defend him by saying he is in an impossible position—the company is doing too well to overhaul, especially just before an IPO. They believe that he will take a much more significant and public leadership role after the offering.

Page, Brin, and Schmidt say they run the company as a triumvirate. Adds Schmidt: "Larry and Sergey have become my best friends. We have lunch every Saturday at [sub chain] Quiznos. Larry rollerblades in these itty-bitty shorts. He still looks like a college kid. And Sergey comes in from a diving lesson. These are special times."

Schmidt understands that investors like to know that someone is in charge—and explains that, in the triumvirate, his is the last word. "We seldom disagree," he says. "If we do, we put it to a vote and whoever gets two votes wins. If it's a particularly egregious disagreement and it's important enough, I'll override them and they'll be mad at me for a while." What about the fact that Brin and Page control large amounts of stock? "They have the final trump, but they'd never use it—then they wouldn't get to see all the people they've gotten used to eating lunch with," he says, implying that he and the people he's hired would leave.

It's not likely that the internal issues will scare off potential investors; what great company hasn't had hiccups on the way up? But it isn't the best time for Google to show vulnerability—not with the big boys on the Internet determined to win its users away. The most immediate threat is Yahoo. It's expanding into new areas like product search (helping people to find goods, read reviews, compare prices, and buy) and local search (enabling users to find a plumber or landscaper in their neighborhood). Google has prototype sites that provide those services (froogle.google.com and labs.google.com/location), but they're not nearly as good. With about a 5% stake in Google, Yahoo goes quiet when talking about the company. Yet it's likely Yahoo will dump the stock after the IPO. Even sooner it will stop using Google's search on its site, relying instead on its newly acquired units. Says Jeff Weiner, senior vice president in charge of search: "We have every intention of deploying Inktomi and Overture throughout all our search."

Then there's Microsoft. The company has an army of brainiacs working on incorporating web search into MSN and its new operating system, code-named Longhorn, due out in 2006. It plans to be able to index every user's hard drive and use the information to provide better searches. "All I'll say is that search is vitally important to us," says Chris Payne, Microsoft's executive in charge of search.

Other competitors could jump into the fray soon. Executives at America Online, Google's biggest partner, accounting for roughly 10% of its revenue, have in meetings expressed concern that Google has become too powerful to keep as a partner, according to a high-level financier who was a party to the conversations. The problem for AOL is that while Google supplies it with valuable search technology, which AOL doesn't have, it is starting to compete with AOL in products AOL does have—like news. Ultimately that could enable Google to siphon off traffic and advertising dollars. "AOL's concern is that Google wants to be a portal," says the source, who has been on conference calls with AOL's search chief Gerry Campbell. (AOL, which is a unit of FORTUNE's parent, Time Warner, would comment only that "Google is a very important partner, and we look forward to continuing to work with them.") In mid-November, AOL announced it was beefing up its search capabilities by buying a Seattle startup that specializes in audio and video search.

The other Internet heavyweights, eBay and Amazon, see Google's huge user base, its growing push into commerce, and—soon—its need to keep Wall Street happy as potential threats to their businesses.

So is Google, as they used to say about Amazon, toast?

Doubtful. But the fight to stay at the top will be brutal—a sobering thought for those waiting to buy in. After an IPO, Google will have mounds of cash, but money alone won't hold off the likes of Microsoft. It's easy to picture Microsoft using its Windows monopoly to lasso people into using its search—even if its search is slightly clunkier than Google's. That scenario won't happen, says Brin. He thinks the company with the superior technology will triumph: "If they force users to use MSN Search and it's inferior, it will cause lots of problems for them." Instead of locking in users, Google will go on creating services that keep them coming back voluntarily. He points to Google News, where users can sign up to be e-mailed whenever a story appears that contains a word or phrase they're interested in. "I wouldn't pursue anything—what's the buzzword? sticky?—for the sake of having something sticky. Users will put up with it for a while, but at the first opportunity they'll change. So I'm not a big fan of handcuffing," he says.

It's typical Google idealism. But then, the founders have proved that the Google culture can create opportunities where conventional wisdom (and experience) sees none. Soon, though, whatever they do will have to be done with shareholders in mind—a prospect that makes seat-of-the-pants governance impossible. Of all the searches done on Google, one that can't yet be answered is whether this company is ready for prime time.

Feedback: fvogelstein@fortunemail.com