what kind of cable have you got? name and model please.
I'll look it up and get back to you.
Usually, the ethernet cable coming from the Wii Lan Adapter connects to your internet enabled router, a router which acts as your modem and switch allowing internet connection of multiple pc's and data sharing with each other. If, however, you do not have an internet router but rather just a simple broadband modem, then you can always connect your wii ethernet adapter to your computer's ethernet port to create an internet sharing relationship (which is more work for you and more hassle having to have the computer on to use the wii internet).
NOTE-you can plug your ethernet cable from your wii to your modem directly but is not very ideal for long term usage as it will void your computer of internet use and will result with you pluging cables in and out to connect the right device to the internet upon request. Unless you are ok with all that hassle and only need the wii internet occassionaly for updates.