Are all of your fans spinning in the computer? Is the inside clean of dust, especially around the processor and heatsink?
I would run memtest My linkhttp://www.memtest86.com/
on your computer overnight. If you need help on installing that let us know.
Are you sure that it is a hardware issue? If you go into task manager, do you ever see the cpu usage spiking? I would suggest backing up your files and reformatting/reinstalling the hard drive, or at least restoring it to factory settings, but only if you feel comfortable doing this yourself.
An issue like this could be caused by almost anything really. I've seen similar things happen to computers with failing hard drives, power supplies, or motherboards.
"I think there is a world market for maybe five computers." - Thomas Watson, Chairman of IBM, 1943