Hi koolkat77,
Starting from the top:
I haven't overclocked my computer to my knowledge; I'm not even sure how to. However whenever I load up the BIOS configuration screen on boot, I see it's often running in "Enhanced Mode" which might change the clocking speed, it seems to default to this every now and then.
I've never noticed the speed getting so high as 3502, though.
I haven't been running any AV software since I uninstalled Avast several weeks ago. I'll be installing MSE after these scans complete.
I've run TDSSKiller with no results.
ESET is currently scanning.
Last time I attempted a Malware Bytes scan (I haven't accepted the Pro trial) I got a BSOD partway through.
I'll try again after ESET completes.
Crystal Disk Info:

"Good Health" it said.
I've got Memtest, and the Seatools diagnostics tools burnt to CD's. I'll run those after ESET finishes scanning.
Thanks again for your help. I'll keep everyone updated.
It's never anything simple, is it?
EDIT #1 - 12:03 PM - I am unable to modify startup files as I'm in safe mode; running too long in normal mode causes BSOD's.
EDIT #2 - 12:27 PM - ESET completed the scan. 3 files were found and deleted, though each of them seemed to be adware. One was CrystalDiskInfo, so that shouldn't have been responsible since I downloaded it an hour ago. Attempting MBAM now.
EDIT #3 - 3:22 PM - MBAM completed a scan, finding 3 other files. These had been on my system for a long time, however. Still deleted. Seatools diagnostics turned up no major issues either.
I've unplugged all peripherals except for mouse and keyboard, I'll run a checkdisk and memtest tonight overnight.
I can't be sure what caused the crashes before. I'll just wait until they happen, or don't, then I'll post another update.
Thanks again. Even if I didn't find an obvious issue, it's soothing taking steps to resolve an issue, and comforting to know people are willing to help.