Double check the MB settings for your memory. Verify the voltage is set manually correctly, not picked up automatically. Set the timings manually, do not let the MB pick them up from the dimms. If it doesn't stabilize set looser timings and see if the system stabilizes.
You are more likely to have a bad dimm then to have a bad MB.
"...will run fine on either 4GB memory chip and it does not matter which of the two slots I have the memory in, but if I try to run the machine on both 4GB memory chips, blue screens return.... " Did you try to isolate to a bad dimm, or just a bad dimm slot ?