Well, I'm at about the end of my rope. I bought a new computer in January and an Radeon HD 4870 to go in it. All worked well for a few weeks, then I started getting BSODs, most of them of the IRQL NOT_LESS_THAN_OR_EQUAL kind and a lot of the time they went back to ATI files, so I assumed it was a driver issue. I uninstalled all drivers and did a clean install. Worked for a shortwhile and then I started getting BSODs again. I got annoyed and figured I screwed something up and reformated. That worked for two weeks and then it started happening again, last Saturday.
The BSOD of originally started while playing games, then they'd also happen randomly for no reason (on the internet, leaving the computer idle, etc.) and Saturday it happened the sameway as before and then again immediately after. I thought it might be a PSU issue so I replaced it with a better one (same errors occured before and after) and I've ran memtest86+ for 9 passes (left it on all night and while I was at work) and it found no errors with RAM. The BCCODE for the errors is rarely the same, going from D1 to E7 that I remember and didn't always reference the offending file (Saturday the first time it referenced nothing and then the second time it referenced an ati file).
So could a bad graphics card do this or am I looking at something like a failing harddrive/motherboard and how could I test to see which? I would just take the graphics card out and see if it crashes anymore, but since it's very sporadic I don't know that it would do any good.
My setup is
PSU 680w
AMD Phenom 9650 Quad-core
8GB of RAM
Windows Vista Home Premium 64-bit
ATI Radeon 4870 (Manufactured by HIS) with CC 9.3 installed (it hasn't crashed yet with it, but it didn't crash immediately with the other CCs either)
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I'm assuming you've run scandisk, defrag, virus scans, addware removal, etc. and not turned up anything significant?
Try reformatting again and see if it makes all the problems go away for a week again.
If you're convinced it's hardware related then maybe you can stress test other components (video/harddrive/?) like you did for RAM.