It sounds like a bad stick of memory. If you can get the PC to boot to BIOS, set the 1st boot device to the DVD drive and reboot with a Memtest CD in the drive. It will run a memory test on the RAM stick(s). It's best to check one stick at a time. http://www.memtest.org/
Download the ISO file and burn the pgm to a CD. It will produce a bootable CD you can check memory with. Let it run for several hours or until it shows errors.