I've bought a GTX670 so I suppose I could try the same thing in my situation too.
Basically I've been having a lot of BSODs for a while now with various error codes but all to do with ntoskrnl.exe (which doesn't actually diagnose the problem). I can reproduce a BSOD every single time by simultaneously:
1) transferring a Diablo 3 folder from HDD1 to HDD2
2) transferring all the program files from HDD3 to HDD4
3) playing music while I do so.
I'm not sure which or if all of the above are necessary, but it's never been able to complete the entire lot successfully. It's just what I'm doing to test for stability anyway since this can reliably tick it off while memtests and intelburntests don't pick up anything. Prime might do it eventually but that will take too long.
I've used various system images and even an old system HDD that still had my C:\ from my pre-ssd days, and they all give the same errors. I'm fairly certain that it's my mobo/cpu/ram that's causing it, but I suppose it doesn't hurt to put in my gfx card and replace the HD5870 while I'm at it.
I didn't really want to replace that combo until the end of the year, but if it comes down to it.. I'm fairly happy to do so. I'd be looking at an i5-4670, maybe an Asrock Z87 Extreme4.. haven't sorted out the ram yet, but probably something 1866MHz. I think a slim profile Noctua CPU cooler would be the most accessible one for my purposes. Promeltech and Thermalright stuff are rather hard to find.
Let us know what you find Ani. You suggest that you've got a high suspicion that it's the graphics card, but you can't really confirm that until you've replaced it.