First Time Build, Memtest86+ errors

This is my first time building a computer from scratch and I'm having major problems. Here are my specs before getting into my problem.

Antec 900 case
AMD FX 6-Core 6200 Processor
Gigabyte GA-970A-D3 motherboard
Corsair Vengeance DDR3 1600mHz 8GB (2x4GB) RAM
XFX Radeon HD 6850 Video Card
OCZ 600W ModXStream-Pro PSU
OCZ Vertex 3 120GB SSD
Ideazon Merc Stealth USB Keyboard
Logitech G5 Mouse

The problem I have been having is getting BSODs when playing games. I started running Memtest86+ and got errors on test 5. I RMA'd the memory but the new memory has the same exact problems.

I tried using 1 stick of RAM at a time and got even more errors, regardless of which memory slot I used, to the point where 1 of the RAM sticks wouldn't work (won't boot) in the blue memory slots, only the white, but either way I get MORE errors by using only 1 stick vs 2.

I also tried memory, PC3-8500, that I had in my Dell XPS 430 and got the same errors, even though I get no errors when running the RAM in the Dell.

I'm at a total loss here, all of my drivers are up to date, I've flashed the BIOS and flashed the SSD.

I've also tried using the auto settings for the RAM latency and voltage in the BIOS and I've set them manually based on Corsair's SPD, but still doesn't help, I get a minimum of 2 errors in test 5 on each pass.

Any ideas or suggestions on how to find out what the real problem is since at this point I don't think it's the memory, but I'm leaning towards the motherboard, which I've already had to RMA once because of a bent transistor.

Thanks for any help.