Computer Shuts Off

I am running an AMD Athlon 1.83GHz with 256MB DDR ram and a gigabyte motherboard on Win XP PRO. My problem is that the computer will shut off during use and power down completely to where the led lights on the case are off. The motherboard is getting enough power however to light a small led ligh near the ram. The computer then wont turn off until I switch off power to the power supply and then it will turn on, boot up part way and then die again. After leaving it sit I have gotten it to run long enough to boot into windows and do about 30 minutes of disk defrag. Does this sound like a power supply problem? Any help or suggestions would be greatly appreciated. Thanks.