Ok, the next logical thing to test is the cpu. Same as the ram, different cpu in the board, cpu in a different board. But understandably this is not always possible, not many people have spare cpu's/motherboards lying around. You can get a compatible sempron 140 for $4.50 on ebay.
I do have some easier things you can try first though.
Disconnect everything except what is needed to boot, no hdd's no peripherals, no fans(even the cpu fan) just the motherboard, cpu, gpu and power.
Try without the gpu, i know there's no integrated graphics but if could tell us something.
See what the battery does.