I haven't tried what you suggested without the GPU yet, but I think I have singled out the problem. I don't believe it's a memory module but instead one of the memory slots on the motherboard. No matter what module I use the computer wont POST if it is in slot B1. However, it will post with memory in A1, A2, and/or B2. Does this mean that I have a faulty motherboard?
It certainly seems to indicate a faulty memory slot.