Ok, time for an update. I'm posting this from another computer, because my computer now refuses to even start up. However, I was able to get some results from running Memtest before that happened.
After 6 hours and about 6 passes, I came back to find over 350,000 errors reported. Now, I just put in some new RAM yesterday, so it can't be the RAM going bad already, I don't think. Add that to the fact that my computer doesn't want to start up, could it perhaps be a bad motherboard? Could a failing hard drive cause these kinds of blue screens and stuff?
If anyone could provide some further assistance as soon as they can, i'd really appreciate it.