Full Range of BSODs-Suspect Hardware?

Hello Computer Aficionados,

I've been having some difficulties with my desktop:

Windows 7 Ultimate/Small Ubuntu Partition (30Gb)
AMD Phenom II X4 B60
AsusTek M4A88T-M
2x8Gb GSkill DDR3
ATI Radeon HD 4250 (Integrated Graphics Card)
PSU: 350W

I received this desktop from an acquaintance, and it worked stably for a brief time (the first 2 or 3 months) and it has since began generating BSODs seemingly at random. However, I can trigger a BSOD by running a video game (even on low graphics resolutions). The game will run for a brief time, between 2 and 5 minutes, before ultimately bluescreening into any of a multitude of different stop codes, I've attached the 6 most recent minidumps.
Additionally, I've run a few Prime95 torture tests and they all crash the computer in a manner of seconds. Prime95 also crashes Ubuntu when I attempt to run it on my Linux partition. While I am not particularly skilled in computer troubleshooting, so please correct me if I am wrong, I feel as though crashing across multiple OSes is indicative of a hardware failure. That being said, I don't know what is failing, I've run 5 passes on each of my RAM sticks separately and nothing has come up.
I would be greatly appreciative if anyone had the time to help me diagnose and fix these errors. This is my first time on a help forum, so if you need any more information that I can provide please feel free to ask away.

Thanks Again
 

Attachments

  • 6 Most Recent Dumps.zip
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I believe it is a hard drive issue. Do you see any yellow exclamation points (!) in the device manager?
 
No, (!) in the device manager, but the computer does have an old sd card reader that doesn't function correctly-I hadn't thought about it but could that be the root cause?
 
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