Can't get Wii to hook up to wireless internet?

I live on my college campus and I'm trying to hook it my Wii up to the dorm Wi-Fi. I tried both the password secure (which is what my laptop and iphone use) and the non-password secure Wi-Fi (which is for people visiting campus mainly) but the Wii won't hook up to either of them. I've made sure the security type and password are correct for the secure connection. Every time I try I get a code 51330, 51331, or 51332. The Nintendo support site only says to keep retrying the password or check security type, which I've done multiple times. I know console devices can hook up to the internet since multiple friends in my dorm do it, but they can't figure out why my Wii won't connect. Can anyone help?

Added (1). I know for sure they've hooked xboxes up, but I'm not sure if my friend has hooked her wii up. If that's the problem is there a way to fix it?

Have they hooked their Wii's up to the Wi-Fi or do they have different consoles hooked up? If I had to guess I'd say the Wii is hooking up to the Wi-Fi correctly then when it goes to test the site it gets redirected to your university page asking you to login, but the Wii's not smart enough to know that and assumes it can't connect and disconnects you.