Can Google (GOOG) regain some of its start-up mojo? That seems to be the focus of founder and new CEO Larry Page, who took over from Eric Schmidt in a bid to shake up the organization.

Back in August 2004, following its closely watched (and unusually democratic) IPO, Google stock shot up from $85 to just shy of $715 per share by December 2007. But Google today is by no means the scrappy little company trying to change the world. Employee headcount is up to 23,331 full-timers.

Google is by no means suffering. Third-quarter revenues came in 23 percent higher over the previous year to $7.29 billion, largely on traffic at its own sites (67 percent of the total). Its AdSense program, which manages advertising for others, contributed another 30 percent. Interestingly, more than half of income came from outside the United States.

At least some analysts see good news ahead. "We believe results next week should come in well above current consensus estimates on accelerating growth in traffic to the site and improvements in monetization," Canaccord Genuity analyst Heath Terry said in a recent note. He’s targeting $800 a share.

Schmidt’s departure has been widely commented on, yet the fundamental question about the stock hasn’t really changed, regardless of who runs the show: Can Google be more than a search engine company?

Here are two areas where Page and Co. are definitely in the running:

Mobile

Google’s Android mobile operating system will by 2012 control half (49.2 percent) of the market, according to Gartner. The growth will come from massive adoption of smartphones around the globe, hitting 468 million units in 2011, a huge move upward from the 296 million units in 2010. Why so fast? Android is “free,” or nearly so, to developers and hardware agnostic. Some folks were putting it on tablets more than a year ago.

Office

Google would love to displace Microsoft (MSFT) in a potential post-PC world in which most users interact with the Internet (and thus Google) via tablet-based browsers and mobile phone systems. The missing piece is a functional office suite. There, Google has stepped up with improvements to its Google Docs offering.

Nevertheless, Microsoft is charging into the virtual software space as well in a bid to keep its lucrative Office product suite relevant to corporate IT buyers.