A new Dell dual core AMD machine with 1GB of memory was going for $329 last week. At those prices, I'm no longer willing to spend a whole lot of time troubleshooting old hardware.
Other than that, I can only give you the standard advice, start from the wall and work backwards. You can't tell anything about the motherboard until you swap out the power supply. The only other thing to try is to disconnect everything that's plugged into the motherboard that you can and see if one of them is preventing it from starting up.
Let us know how your APC five million dollar lifetime connected equipment warranty works out.
Matthew