I recommend using a free program called
MemTest86. The download will make a bootable CD or diskette (your choice), which will run 10 extensive tests on the PC's memory automatically after you boot to the disk you created. Allow all tests to run until at least three passes of the 10 tests are completed. If the program encounters any errors, turn off and unplug the computer, remove a stick of memory (assuming you have more than one), and run the test again. Remember, bad memory cannot be repaired, but only replaced.