A full story and fine details of the machine may help. Some of those older Athlons are dieing due to neglect (cpu heatsink falls off) or other issues.
The wild guess could be motherboard, cpu, video card, hard disk, CD/DVD failure too. You don't know till you strip it down. Here's some troubleshooting guides.
http://www.google.com/search?hl=en&q=TROUBLESHOOT+A+DEAD+PC&btnG=Google+Search
Bob
My computer just suddenly turned off by itself, without any warning, and then I can't turn it on again. The led on the motherboard still lights up but just won't power up. Is this a problem with my power supply or something else. thank you

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