error checking can miss problems with hard drives
http://www.memtest86.com/ download that and then use IMGBurn to burn it to a CD and boot from it. (this will test your memory. memory rarely goes bad, but it is possible)
Do you get any beeps when you start up the computer?
What Brand / Model computer is it?
Your MoBo could be bad too. (Does your MoBo have an error log in the system setup?)