Do what Route44 suggests. Does your system even begin to load the OS? Are there any beeps from the computer before it shuts back down?
I would say it's probably the PSU, where it provides enough power to allow the motherboard to test the functionality of all parts and get past POST but once the OS loads and powers up all the peripherals (CD/DVD drives, USB devices like your mouse, hard drives, floppy disks, video cards etc.) your power supply fails.