Kdirksen
The ME516-3, -8, -11, and -12 refer to different memory pattern tests that are failing. For example, ME516-3W = Auxiliary Patterns Test.
Several things could be wrong besides the memory itself. It could be a misconfigured BIOS, a bad shared memory video card or, as you fear, the motherboard. From the errors you are receiving it sounds like you have an HP system. I would suggest contacting HP or consulting a qualified technician to further investigate this issue.