do you have a cable modem?
do you have multiple computers already connected to your router?
cable modems require a specific MAC address. if the router isnt cloneing the correct MAC address (or none at all), then no other computers/consoles will work on the internet.
if you already have multiple computers already connected to your router and are working properly, then more than likely something wrong with your ethernet cable, LAN adapter, or Wii
i hope i helped, or at least led you in the right direction