I have 2 computers with very similar problems.
My first computer is an HP Slimline s3127c dual core AMD processor with a small form factor case. One day it just stopped turning on. When I press the power the power on LED lights up for a second but doesn't POST. Fans run though.
Did the usual, re-seat memory, de-dust it using compressed air, re-seat cpu, remove BIOS batter but it still won't POST. After unplugging it and leaving it in a corner for a few days, I plug it back in and try booting up and it works this time. It consistently boots for the next few weeks then does the same thing again.
Figuring it was time to get a new computer anyways I bought a Acer Aspire X3400. All is good for 3 months then low and behold I have exactly the same problem as the HP. I plug in the HP again, and again it boots.
I'm starting to think it's a PSU problem but am not sure. What do you guys think?