You should also test the hard drive, not just the RAM.
All the major drive manufacturer's make testing software available on their respective websites. Links here:
http://www.tacktech.com/display.cfm?ttid=287
The Seagate testing software will actually test any make of drive if you can't ascertain the brand of your drive, using "generic tests", but using the appropriate software for that brand will be more thorough and reliable.
If you see any "Failed" entries during the test, you need a new drive. Be sure to run the "long" test where available as the short test doesn't check as thoroughly.