This started happening some time ago and I've never been able to figure out why. After I shutdown my computer, I will be unable to get it to power up again unless I turn off the power switch on the back of the power supply (or turn off the power strip) and let it sit for several minutes. By 'not powering up' I mean that it won't even get to the POST mode where the motherboard 'beeps' and it loads the BIOS. The power LED will be "ON", but the fans will have all turned off, and the reset switch does nothing in this state.
Thanks for any help. I have a friend this exact same thing is happening to as well!