Faulty memory can cause many problems including "kernel panic" errors, and memtest86 is an excellent tool for diagnosing memory problems.
Zip files with the iso can be downloaded from http://www.memtest86.com/ .
Extract the .iso from the zip and burn it to a CD with burnatonce. Put it in the CD drive and reboot. When the system boots from the CD, memtest will evaluate whether there are any problems with the RAM. It could take a while (up to an hour) to run.