What if you remove and reseat the RAM and all cards in the machine? If no joy, the next thing I would do is disconnect all the drives and and remove all of the cards except the video and see if it will boot. If it does, add one thing at a time until the culprit is found. If not I would test the RAM (
www.memtest86.com) if possible in another machine. If that cannot be done, then the suspects are motherboard, CPU or RAM (going on your assertion that the PSU is good.
Perhaps a local shop could test the CPU. If OK, that would be the motherboard as the most likely suspect. Do you happen to know the processor type and speed? Do all of the fans, especially the CPU fan come on, at least initially, or is there enough time to see?