This is a hardware question, and should be moved.
Pull two of the 4 sticks of RAM and re-run the tests. If no errors, you know the bad stick(s) are off the system. If you get errors, pull one stick and re-test. Continue troubleshooting until you determine which sticks (if any) have errors.
If they are ALL bad, I'd look at motherboard, power supply, etc... If none are bad, same.
Any chance the RAM is undervolted ? What's the default voltage on the M/B and what's the minimum on the RAM.
Is the system overclocked ? If so, back it down to factory spec.
Also, check BIOS and verify that the default timings are at the RAM spec.
Is this 4 sticks of 1 Gbyte, or 2 sticks of 2 Gbyte ?
Is this the RAM ?
http://www.newegg.com/Product/Produc...ILL-_-20231112
NewEgg reviews show this RAM may have a problem with errors.
http://www.newegg.com/Product/Produc...82E16820231112
But I wouldn't assume that because a few disgruntled NewEgg reviewers have problems, that your RAM is bad. Some of these reviewers are complete idiots. However it sometimes gives you a direction in which to consider.