I just has a similar thing happen on a computer here in the store.
If the computer has a video card that requires power (ie: AGP GeForce 6800) try disconecting the power to the card and turning the computer on. If it powers up, You have a bad video card.
If that doesn't do it, try disconnecting the hard drives, fans, etc. one at a time and repeat the process.
It's actually unusual for a power supply to go bad.