How would you troubleshoot this?

I have a p4-1.5Ghz chip on an Abit TH7 board with 256MB memory and a 300Watt powersupply. My system will not even power on. When I turn the power on, the monitor receives no signal, but everything spins up. Internal system lights light up, fans turn on and all that. I've replaced video cards and the monitor, but that doesn't seem to be the problem. I've had past problems with an overheating chip, CMOS checksum errors, and other fun stuff, but my system just now blew up completely, and I'm not sure if I should replace the chip, motherboard, memory, or PSU. I don't have spare parts for these, and would really rather not buy parts I don't need. Any suggestions?