Ok i bought a wirless router (linksys wrt54gs) to get online and at first it worked fine then didnt even though i was picking up a signal i kept getting error codes other people were like 53020 or something similar. anyway i know a lot of people are getting problems with linksys products. i tried this and it works fine so try it and see if it helps.
First power up your wii then clear the connections you have had or tried. then UNPLUG the router for 30 secs and reconnect it and then try and connect the wii. for some reason this seems to work everytime for me but when the wii has been off and the connection is reset it doesnt seem to connect.