Computer shutting down

I have a refurbished ThinkCentre 9210 Desktop PC Pentium 4 3.0GHz 1GB DDR2 40GB HDD Capacity Intel GMA 950 Windows XP Professional that I bought from Newegg.com for ~$125 dollars, it worked fine for about 6 months and just recently it started shutting down randomly. Trying to figure out where to start trouble shooting. I don’t think it’s the OS because it will shutdown even when I but in a Linux live disc and there are no errors in Windows event viewer. I’m thinking it might be the power supply, cpu overheating, or maybe the memory. Any help is appreciated.