I'm going to keep this short. Here's my video card:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814125333

Here is my PSU:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139011

Here is my motherboard:
http://www.newegg.com/Product/Product.aspx?Item=N82E16813128437

Processor:
http://www.newegg.com/Product/Product.aspx?Item=N82E16819115214

Here's the problem:
When I run my computer with 0 of the 6 pin connections going to the video card it runs fine, the fans on the video card run and everything. When I plug the 2 6 pin connections to the video card the computer does not run and the fans spin up for like 1 sec and stop and then it repeats this. Also, If 1 6 pin connector is connected in either of the 2 6 pin ports it works fine. It only messes the computer up if both are plugged in.

I was thinking that this meant that the PSU was not powerful enough, but I used an online PSU wattage calculator and it says that 850 watts is fine.

What exactly is the problem?
I do not know if the video card is outputting a signal because my monitor has not arrived yet.

 My motherboard does have a speaker. When this happens it starts to make a noise but the power cuts out.

I was thinking this is a power supply issue, but I just can't be sure.

I've decided to RMA one of these. Any suggestions as to which one I should RMA? Video card or PSU or both?

Umm how?

I have made a breakthrough in this. It's not the video card or the PSU, it's the motherboard.

If you read the motherboard reviews (the 1 - 3 star ratings) people with this motherboard have been having the exact same issue.
It appears to be an issue with the 8-pin connector, but I don't know how to fix it.

Any suggestions?

Read reviews before you buy things in future. RMA that MF.

I find your logic quite unreasonable. On this particular motherboard there are only 3 reviews complaining about this. On some other Gigabyte motherboards there are people complaining about it but why would I look into those boards? I've been using Gigabyte motherboards for years now and never had any issues.

Also, I don't think the board is dead. People have said that they RMAed it several times and still had the same issues. Do you really think that Gigabyte has that many faulty boards? Maybe I'm just doing something wrong.

Remember, it runs fine when my video card isn't hooked up...

I re-seated the CPU and everything works now. Queue the laugh track.

man dust either you fix computers for work or you're the worst person ever with computers given how many problems you keep having.

you're the worst person ever with computers given how many problems you keep having.

=(