Ive had the problem you are all experiencing before. Before you worry about changing anything else, reseat your RAM. I did this and it fixed the problem. If not ram then most likely CPU. More than likely its not the PSU due to the fact that it is starting up. Your computer goes through a series of checks upon startup and if one of your components arent working it will shut off completely. The first component that does anything is your BIOS chip. It takes information that is stored in your CMOS battery and it tells all your other components how to function. (clockrate etc. You can change these in BIOS.) from there you check your CPU (processor). Your processor communicates with a chipset called the Northbridge which in turn communicates with your RAM and your video card. It also communicates with your southbridge which in turn communicates with every I/O (input/output) device on your system. It could also be your motherboard. One of the most annoying issues to troubleshoot in my opinion.
-reply by Hewitt