Computing today is still in its infancy, Microsoft Chairman Bill Gates told a full house at the TechNet Innovation Summit in Memorial Auditorium yesterday afternoon.

“The P.C. that I dreamed about having for myself is far better than what we offer now,” Gates said, predicting his dream computer might be available within 15 years. “It’s a time when all the large companies have more opportunities than ever before.”

In a wide-ranging one-hour discussion, the world’s richest man talked candidly with PBS anchor Charlie Rose about his company’s competition with Google, his ambitious humanitarian agenda and America’s relative decline in economic power.

Gates hyped the new Window’s Vista operating system, set for public release at the end of January. He called the iPod a phenomenon and said that the just-released Zune hand-held portable music player has special features that make it worthy to compete, including the ability to share songs with friends. While Microsoft came late to video games, he claimed that the new Xbox 360 will be the best console in the industry.

The 51-year-old has made headlines for giving most of his fortune to the charity that he and his wife co-chair, the Bill and Melinda Gates Foundation. Gates talked about foundation goals, ranging from fighting malaria in Africa to improving charter schools in America. With a pledge of $31 billion from investor Warren Buffet this summer, the increasingly influential foundation will be able to spend $3 billion a year by 2009, Gates said.

“The opportunity is there, but you have to put the pieces together in a different way than has been done before,” he added.

Gates, who wore a pinstripe suit without a neck tie, said he was hopeful that the foundation could have a real impact.

“I started naively optimistic,” he said, “and now I’m more concretely optimistic.”

Gates also called China the new “pace setter” for the global economy.

“It’s like capitalism running at a higher speed than it is here,” he said. “We have to renew our commitment to the things that made us stronger.”

He noted that America’s relative economic power has been declining since the end of World War II and that it will continue declining as China and European nations grow. But he said the whole world, including Americans, will benefit from growth and the proliferation of technology in the years to come.

“The U.S. has been sort of spoiled by being powerful for so long,” he said.

When Rose asked Gates about his decision to drop out of Harvard, Gates quickly interrupted to say that he had only stopped out.

“My parents were very concerned,” he reflected. “It seemed like a big risk. It was one of those times that went almost beyond numerical thinking.”

On his company’s high-profile competition with Google, Gates acknowledged that the two firms “overlap a lot.”

“This competition is a fun one for both companies,” he said. “You want two companies with crucial mass taking on tough problems.”

When a graduate student in computer science pressed him about his dim predictions that American students are falling behind in math and computer-science education, Gates showed his softer side.

“It’s actually good for you,” he told the student. “Say there was only one computer scientist. Then we and Google would bid, like, a billion dollars for you to come work for us.”

Rose, who has interviewed Gates nearly a dozen times, said the tech icon was as energetic Wednesday as he had ever seen him.

“He was engaged,” he told The Daily afterwards. “You could feel the resonance that people were into what he was saying.”

The discussion with Gates was the third panel of the day. In the morning, Yahoo! founder Jerry Yang and Netflix CEO Reed Hastings talked about the future of innovation. Another morning discussion focused on energy alternatives and green technology.

John Doerr, a speaker on the Going Green panel and a partner at Kleiner, Perkins, Caufield and Byers, said that he thought the global dimension of the program made the program unique.

“It all comes together right here at Stanford University,” he said. “We’re at ground zero.”

Gates is the public face of Microsoft, a behemoth of a company that some critics charge has passed its prime. But Rose said Gates’ passion for his products and his company showed when he spoke.

“I would never count Microsoft out,” Rose told The Daily. “I would never count Bill Gates out in terms of the end game. They have very good second-half players. They know how to play catch up.”