I have since reinstalled Win 7, and now the crashes are very much apparent. They now go to a BSoD after a 2 minute wait, but no matter what I do, the dump from the crash is never kept.
I was pretty sure it wasn't a hardware issue, but if it keeps crashing like this... I guess it is? Would it be a hard-drive issue that's causing it? I ran scans and formatted both the HDD and the SSD, but I'm not really sure where to go now |: