GPU Problems in my new build?

Here are the items in my build:

Intel 2500k - $179.99

Corsair 4 gb 2x2 1600 - $39.99

Spinpoint - $49.99

This Gigabyte HD 6870 - $199.99

Wireless USB Card - $9.99

MSI P67A-G43 (b3) -$ 94.99 (Including $40 combo with 2500k)

Coolmaster Hyper 212 - $27.99

Samsung DVD-R - $21.99

Coolmaster HAF 912 ATX Gaming Case - $64.99

OCZ 700w ModXStream Pro PSU (modular) - 89.99

I have been having some major problems getting FO3 to not freeze and I get graphical issues in Mount and Blade Warband (the water and skybox get corrupted). I then just tried to play TF2 for a while and it froze. I was thinking that these are game bugs, but I then did some tests. By the way, I am running Windows 7 64 bit.

Windows memory test - fine Prime95 - Fine, temperature stayed did not get above 63 degrees Futuremark GPU Test - Caused system to shut off after about 3-5 minutes of testing. OCCT GPU Test - Started having errors after a few minutes, then shut my computer down.

In both of these tests my computer shut off when my GPU was around 75 degrees, so I don't think that I have a heat problem. What is going on? Do I need to RMA my 6870?

I would think that a 700 watt PSU should be having no problem at all, but if that is an issue let me know.

By the way, I am not overclocking anything yet, so this is not a bad overclock.

Thank you!