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Try disabling the on board video and using a video card. It sounds like it that or the memory. I have worked on a lot of computers like that. I ether had to reseat the card or use another.

Hmmm.... Two problems..
First, I have no idea how to disable it. I don't know the right jumpers. Secondly, a new video card won't work because all the PCI slots are used up, and there is no AGP slot.

If troubleshooting the memory and video card does not yield any solutions with the system then you will need to consider the problem to be the motherboard.

I swaped the memory modules to see if that would do anything, but nothing changed.

Hmm..you think its the motherboard? I never really suspected that. The inside of the computer was never touched since the day he got it in 1998. He told me that he was on the internet, and the computer froze. So he powered it down and when he went to restart it, thats when it stopped working. I've even tried booting it from boot disks and recovery CDs, but nothing happens.

DEAR FRIEND,
THERE ARE MANY POSSIBILITIES.THE RAM MIGHT GOT PROBLEM. THE DISPLAY CARD MIGHT GOT PROBLEM, TOO AS DISPALY CHIP IS ONBOARD, YOU HAVE TO DISABLE IT BY JUMPER SETTING BEFORE INSTALL A NEW DISPLAY CARD.AND ARE THE IDE CABLE IS WELL ATTACHED AND ARE THE IDE PRIORITY IN PROPER ORDER.
COULD YOU PLS TELL US HOW THIS ALL HAPPENED.

Just an idea, is the system possibly overclocked? If so try holding down the insert key at bootup, this resets some mobos to a bootable state.
Good Luck!
Chris!