You have tried everything that I would have done myself - different CPU, RAM, GPU, PSU. The only thing left would be the motherboard.
One last thing would be to take out the CMOS battery and then clear the CMOS via a jumper.
Directions are here...
Sounds like a motherboard problem. You will most likely have to buy another motherboard from eBay since it's an OEM-specific motherboard.
Or you can just buy any MATX LGA775 motherboard from Newegg and it should fit your case. The only difficult part would be the front LED/switch connectors...