Ok, well I got everything working perfectly.
I reinstalled Windows 7 64 bit, and installed the drivers from http://support.amd.com/us/Pages/AMDSupportHub.aspx,
(11.11 Win7 64 bit), and everything is working fine.
I'm guessing it had to do something with the old drivers and the new drivers, but it has been working fine for a few days now (the first day after I reinstalled everything I played for several hours, and my card's temperature even got almost to 60 C, OC'ed to the max and everything), and it works like a charm.
I guess this is a last resort type of thing, but I did need and was planning on doing a fresh install at some point.