“Looking back at the quarter, it’s obvious our model works very well,” Google chief executive Eric Schmidt told analysts. But that model doesn’t seem to change, despite vigorous efforts to expand into non-search businesses such as online office applications and mobile services and to move its lucrative advertising model into television, print and radio.

“Eric Schmidt told us about a year ago his goal is to build a $100 billion company,” says Bear Stearns analyst Robert Peck. “You just can’t get there with online ad revenues alone.”

There’s no disputing Google’s dominance in search. In the U.S., more than 5.3 billion searches were conducted across Google sites last month alone, representing 57 percent of the domestic search market, according to comScore. The problem is that today, nearly 99 percent of the search giant’s revenues come from online ads. That may have to change if Google is to continue to justify the premium its shares currently enjoy. The stock closed at a record $639 a share, up nearly 1 percent for the day, and climbed another 2.68 points in after hours trading.

Speaking to analysts earlier this week, Schmidt said Google is “building deeper ad solutions.”

To that end, the company launched a new ad platform that puts a text overlay in the bottom 20 percent of a video box. There were fears that users would resent the intrusion, but according to the company, “initial user response and feedback have been positive.”

But Google has yet to figure out how to make real money in online video – one of two ad platforms the company says it is most interested in pursuing. Television is the other major focus for Google. The company is now in trials with EchoStar and Astound Cable to bring its auction-style advertising model to TV.

Many analysts worry, however, that this technology company run by three technologists doesn’t have the media and old-school advertising savvy necessary to get much traction in Hollywood or Madison Avenue.

“If they expand into these markets they’ve got to realize they’re stepping into areas where there are very large, powerful incumbents,” says Peck. “They can gang up on you.”

That’s already starting to happen in mobile communications, where AT&T (T) and Verizon Wireless (VZ) have complained loudly about Google’s efforts to snap up some of the last remaining slices of spectrum available for cellphone use.

To compete in display ads — where Google trails behind rival Yahoo (YHOO) – the company was banking on its acquisition of advertising pioneer DoubleClick. But that deal is now tied up in antitrust hearings.

Google is also pressing its advantage in web-based email, online office applications and a online payment system called Checkout similar to PayPal, but none of these efforts are generating much revenue.

“I think that all of Google’s new products have been much less impressive than the original product,” says Laura Martin, an analyst with Soleil – Media Metrics. “To me, they’re still a single product company because they’ve yet to prove monetization of their non-search products.”

No one is saying that Google can’t succeed with its non-search products, just that it hasn’t done so yet.

“We could likely be into 2009 before these businesses will be tangible enough to start monitoring very closely,” says Peck, the Bear Stearns analyst.

Meanwhile, ad-supported search is still paying a handsome dividend for Google and continues to grow at a dizzying pace, with no signs of slowing down anytime soon.

“Google is something of a ‘one-trick-pony’ in its current form,” writes Cantor Fitzgerald analyst Derek Brown. “But what an absolutely extraordinary trick it has proven to be.”