Ran memtest86+ one each stick of mem I have and am only using 2 ags atm.
Used the GPU stress test max temp 47C on 1080p no issues.
Prime 95 nothing reached over 30C but CPU hit 35C.
No crashes from stress.
Ok all of your temps look good, if asus tech support does not know whats happening...
Your best bet for today is try a good quality DVI cable or vga cable check your resolutions settings on your vga card.
If all else fails and newegg will accept a rma, we'll get you a different mobo that will work out much better.
Toms hardware forum has reached its limit of what they can do, and possibly us.
Until we know the cable changing does work or not, we cannot do anything else from here.
UPDATE:
What nvidia drivers do you have installed currently ?
301.10 drivers
If you have this, please uninstall it immediately and try a older version if you get a chance.
When your running bf3 was there any other programs running beside it that would cause the rsod ?
I have a strong feeling it's a software/driver combination issue.
If you have onboard, try that first and let your pc run for abit.
No rsod, but GTX 680 keeps doing it ?
I recommend you call the manufacturer for your card and have them replace the card with stable drivers sent to you.
Good luck and let us know what happens.