It really could be the power supply, your hard drive or your motherboard- had a motherboard fail on me, but it was an old one. As @RealFaction said, be wary of some of the repair computer stores out there, yet some of the local stores (as was for the one occasion so far for me) can be really good. If you've got a friend who's good with computers, got with that person to check things out.
Cyberdevil
Had a similar problem with an older computer in which case it turned out to be some loose part in the power supply. The computer started taking longer and longer to start, and after a while it stopped starting at all. The button flashed, it shut down, same symptoms... if that's it then it's not an expensive fix, I don't think it cost more than $20-40. We had to cut out a piece of metal from the computer frame though to fit a new one . :) Good luck getting that fixed!