I know this has been asked a ton, but I thought my situation might result in a quick diagnosis.
ASUS LGA755 motherboard with Core 2 Duo 2.2 GHz processor. Computer has worked fine for 1.5 years, it is rarely turned off. When I turn it off, it does not want to boot back up -- no beep, no boot. If I keep trying for a while, sometimes I can get it back on and then it continues to work fine until I turn it off again. I have removed all PCI cards and doesn't fix. I removed the RAM and I still get no beep. Does this sound like a power supply issue?
That is sounding like the PSU barely has enough power to run the system. First I would try unplugging and replugging all the power cables to be sure one isnt just loose. After that I would replace the PSU, maybe with a more powerful one.