I have been able to run the tests on the computer in question.
Keeping in mind that there is usually a time window of 1 hour before the computer locks up some of the tests were not able to finish. I did observe some interesting behavior which I'll explain below:
1.) All the drivers
I could find were updated.
2.) Microsoft update was run.
3.) Malwarebytes, VIPRE Rescue and Fakerean were downloaded and Malewarebytes installed.
4.) In safe mode VIPRE Rescue was run. There are two drives: one 64 GB SSD with Windows 7 (C:\ Drive) and one RAID 5 array with four disks (E:\ Drive). VIPRE was able to get to the point that it was scanning the E:\ drive. It continued for at least 2 hours (longer than I've seen the computer go w/out a crash). Windows came up with an error though saying "The instruction at 0x000000007777FD94 referenced memory at 0x000000000009DFSC. The required data was not placed into memory because of an I/O error status of 0xc000000e. Click okay to terminate the program." In the command prompt, the scan had failed. I went to go to the start menu in safe mode and as soon as the start menu popped up it locked and gave a similar message for explorer.exe. After that, explorer closed and the system was non-responsive.
5.) Did the full scan of Malewarebytes. It found one file, a dynamic link library used by winamp to convert files to shn format. Just to be safe, I had the system successfully quarantine and delete the dll. The computer owner said that they could restore the dll if need be later.
6.) Ran Fakerean removal tool once.
7.) Ran disk check on the boot SSD (C:\) with no errors (finished in < 1 hour)
8.) Ran disk check on the RAID 5 array. It continued to the point that it said everything was clear and then it froze. I did a cold boot and the system acted as if the disk check was still scheduled (and, of course, it did not show up in the event viewer).
9.) Ran sfc /scannow once and received "Window Resource Protection did not find any integrity violations."
So, I have some thoughts but most evidence seem circumstantial. For now, I'll keep my mouth shut and see what you all think the best course of action is from here.
Also, I have some hardware components on hand to swap out pieces of the fritzy computer if need be. I'm getting ready to build a similar system though not all components are the same (mobo is different and I don't have a spare SSD but I do have spare spin up drives).