I think the Google founders had a vision of solving a problem. They wanted to make search work right.
(Well, technically, they wanted to get their Ph.Ds - the actual history of Google was that Larry had the idea to download the web and throw away everything except the links, so he did that. Then he had the idea to visualize it as a big eigenvalue calculation on the probability of a random surfer ending up at a given page, and that's where he got the idea for PageRank. Then someone - might have been him, Sergey, or Scott Hassan - got the idea to sort webpages by PageRank, and the results were better than existing search engines, and so they launched BackRub as a search engine. Then Andy Bechtolsteim thought it could be a really big company and gave them $100K to make it one, and the rest is history.)
If you steer towards problems, and do so without fear of the unknown, you'll naturally move towards ideas where you get to define the category. They wouldn't be problems if someone had already solved them! The rest - building a business, making money, marketing it, defining it in customers' heads, etc. - can all follow later.
(Well, technically, they wanted to get their Ph.Ds - the actual history of Google was that Larry had the idea to download the web and throw away everything except the links, so he did that. Then he had the idea to visualize it as a big eigenvalue calculation on the probability of a random surfer ending up at a given page, and that's where he got the idea for PageRank. Then someone - might have been him, Sergey, or Scott Hassan - got the idea to sort webpages by PageRank, and the results were better than existing search engines, and so they launched BackRub as a search engine. Then Andy Bechtolsteim thought it could be a really big company and gave them $100K to make it one, and the rest is history.)
If you steer towards problems, and do so without fear of the unknown, you'll naturally move towards ideas where you get to define the category. They wouldn't be problems if someone had already solved them! The rest - building a business, making money, marketing it, defining it in customers' heads, etc. - can all follow later.