You've got to hand it to my university. They're very good at making things difficult for Linux fledglings at every step of the road.
My Uni uses WPA-Enterprise, which you can read about here
(because I'm not going into the details myself (because I don't understand them all)). It took me some guessing/testing until I got a wpa_supplicant.conf file close enough to get me associated with the access point. Eventually, I got a working connection, although I haven't tested it in the long run. I'd bet I would have to make a few more tweeks to get everything working exactly the way it should without any flakyness. For now, though, it works.
I didn't know you had to pass a hostname manually when you sent a request with dhcpcd, but you do. I probably took a little bit too long figuring that one out, but whatever. I now have internet access on my Arch laptop.
The next step? Find a cool power management utility, preferably a cli utility, and NOT a gnome application.