I have thought this was a hardware problem all along, but there are much more experienced IT guys here.
I will say one thing though it may be the power supply. I have had similar issues with my workstation twice, and thought it was done for. In both cases a new power supply made it come back to life instantly. The second time I put in a power supply that was rated 50% over requirements and have had no issues since.
If it were me I would gamble on a new power supply.