Here's a workaround to the wireless internet problems that crop up, it'll just be dependent on your computer skills and amount of equipment you have laying around. You need to turn your PC into a router, basically..
First of all, you'll need a computer with both a wireless card and standard RJ45 NIC. Linux preferred.
Given your situation, if you can log into your college's network on your PC to authenticate, you can then bridge your two wired/wireless connections with internet connection sharing. So, if you've got wired connectivity in your dorm, use the wired method, and share the connection over wireless to create your own access point without any of the hinderances of the college setup. Your PC will have already authenticated you as a legit user.
vice versa, if you have the USB/ethernet adapter for your Wii, you can opt to share the wireless signal you pick up from school over a wired cable. If you don't have a hub/router you may need to pick up a crossover cable, but it can be done.
A pain in the ass, but it can be done with the right hardware and some free time. If you're in a dorm, and you have a Wii, then you probably will make friends quickly - find the computer geeks and they will be glad to help with a project like that.