Something has died. I would have guessed that it was the PSU, like you did, but replacing it didn't fix the machine. So either it wasn't the power supply, or the power supply took something with it when it died.
Most likely candidate is the motherboard, but it could be the CPU. Given the age of the CPU and motherboard, I'd be inclined to replace both, which should fix the problem - better than spending money replacing the old motherboard with a new copy of the same.