Ahh, sounds a bit more familiar Fallout, I had some issues with my 7950 dual SLI card like that, ended up replacing it. I used to have it run in combined mode, so both cards are sharing the load, then I tried to hook up my TV to one of the outputs and went for separate mode, only to find that it would crash at random times. I'm sure that one of the GPU's failed, so in combined mode they would work, but the extra they needed to work separately was just too much.
I think it's a flawed design, dual SLI or whatever they call it - my brother had the same issues with his identical GPU about 6 months after mine.
I say you should try and swap the GFX card, even if it's a cheap and nasty £30 job - trying to narrow down the issue will save you a lot of money, I know, I've not long spent a fortune fixing a cheap problem (replaced my whole PC then later found it was a memory issue all along). Trying a cheap but stable card should tell you if it is your GPU, and then you can spend a third of your budget on a new GFX card, instead of what might end up being a mostly sideways upgrade.