When you first setup your Wii and you go thru the settings, the one thing to do when asked to input a password or key, after the ap is found, is to input the KEY not a password. The wep key can be found by accessing your router info. See your router manual on how to access this info. all models vary.
Since my son got his Wii we tried all the info on the internet to solved this problem . Well it dawn on me to try inputting the key instead of the password and VIOLA!!! now we're on line wirelessly!!! It seems that all Wii's will accept ANY 5 character PASSWORD, but that WILL NOT get you on-line!!! You MUST input the wep key for security purpose.
Hope this helps, it did for me...