Hmm, in this case then, it is possible yes. If you didn't mention the hard drive, I would have expected it to be the sound chip at fault... though it is possible this could have happened.
By any chance has it been switched off? Go into Bios and check.
At least when you get a new power supply, and it works, you know this was the case
If not, sound cards are rather cheap now for excellent sound anyway, which would beat any onboard sound available.