I used to have something similar to this one (the DSL-G604T) before I sold it and got a Netcomm NB5+4W.
The fact that it can find the Router, but not connect to it, suggests that you maybe turned on MAC Address filtering and didn't add the Wii's MAC Address to the filter. Add the Wii's MAC Address to the filter, or turn the filter off. Let me know if this solves anything.
On a side note, use WPA instead of WEP, unless you have a DS and require WEP for that. WPA is more secure then WEP.
23/06/2008
Super Smash Bros. Brawl
"Populating Tag Error" upon visiting Page 2 of Robtot's Comics :/