Diagnosis: fan is dying. Need a new one. Yay sentence fragments.
Computer is working again, though I can't say the same for the fan (or the network card, but that was my own fault). Dell only sold the Studio 14z for a short while, so finding a replacement fan is proving difficult.
I have found a replacement fan, though I won't get it until after finals. That's fine, because I'm not planning on updating anything until finals are over anyways.