First, thanks for all the replies. I've tried taking out hardware and shit like that and nothing seems to make a difference in how this bitch runs.
OK, so all I've been able to come up with is one little thing. Both times this thing randomly rebooted I got this error in the Event Viewer in Administrative Tools:
I've Googled around to see what I can come up with, but I have no clue what the deal is. Does anyone have an idea?