Dave's theory is that the HDD could be corrupting pagefile contents, which go into memory and cause these issues.
I'm not convinced that is plausible, though.
1. all the failures are in dxgmms2.sys, and it seems very unlikely for arbitrary HDD corruption to cause that.
2. Disk Drives have error correction. If the data they read is corrupted, they won't actually send it as the result of I/O and will retry the operation. if they can't read the data without the ECC triggering they will eventually fail the read operation- At which point, I expect, there would be a BSOD surrounding the virtual memory manager.
Given your new information I think your assessment regarding the power supply could be correct. Removing drives would reduce the load on the power supply, and Graphics cards are the greatest consumer of Power in many modern systems. It could be the PSU just can't handle the system when under load and the Graphics card is the component that has trouble as a result.
(You don't mention what the current power supply is, by the way
)