Alienware M17x R3 crash problems

First off, my rig's key specs:

m17x R3 - Intel i7-2670QM, 4GB DDR3, Radeon HD 6870M.

I've had it for 5 months now, and recently when I boot up and any time from on the windows login screen to shortly after logging in and starting to use the computer, it just shuts down. I've gotten a BSOD twice, and it was a 0x1000007E caused by the atikmpaq.sys. However almost every single time, it has not created a dump file and just shuts down immediately without hanging up. I've run the diagnostics through the system startup that the laptop comes with, and all the hardware checks out. 

I've tried wiping the drivers, using DriverSweeper, and reinstalling the Dell drivers appropriate, but the problem persists. I've even reinstalled Windows 7 fresh and nothing helps. When the drivers are completely wiped, or in safe mode, there are no crashes. I'm at my wits end trying to get my system working properly again, but have found nothing of help on dell's support site or searching the internet. Some have suggested installing drivers from AMD, and those cause the same problems.