Not to get too off topic... but it's not a loose connection, because when the case is vented (opened totally, or a small crack, etc.), it works fine for as long as it's plugged in. As soon as you close the case, it starts to reset after the heat has built up sufficiently (15 minutes or so). It's hard to see, but in the current case, there are absolutely no air holes—at the time I didn't realize how hot the sid can get!
I will be listing it soon for the cost of the components and I'll be throwing in a couple of cores I didn't use and some other assorted parts that would be helpful in putting it into a new case. Thanks to everyone for their input!