I've seen similar posts with this issue, but none of the suggestions have helped me resolve the problem.
I had a home-built PC until one day when the CPU overheated and the whole system refused to boot. I checked the CPU and it looked fine, so I salvaged an old Motherboard from my brother's PC (he upgraded). The system wouldn't boot, but the CPU fan and one case fan would spin for a couple of seconds. So I replaced the CPU with an older P4 (went from potentially fried P4 2.4GHz to P4 2.0GHz). Same problem. Thought it might be the Power Supply, so I bought a new one (550W Thermaltake, 200W larger than orginal PSU). Same problem. Replaced CMOS battery. Still same problem. I've upplugged all components save the video card (ATi Radeon9700), and I still have the same problem: CPU fan spins (if pugged in) for a couple seconds and monitor goes from standby to awake to standby. The CPU heat sink is correctly installed/seated using Arctic Silver, and the room is cool. I have 3 DIMMS of 512MB RAM that I've swapped out and tried.
My next step is to try the boot without the video card, but I don't think it's the problem.