It boggles my mind how people attempt to create a home network. It really is worth the price to do it right.
There are at least two things you need to look at. First, make sure the LAN lights are on and flashing between the Wii and your computer. If they are, good. If they aren't, then you need a crossover cable.
Once you have those lights coming on when the cables are connected, you next need to enable internet connection sharing. I'm assuming you're using Windows XP. You enable connection sharing by clicking start, going to control panel, click the link to go to classic mode if you aren't already, click the network connections icon, right click the connection that is using USB, go to advanced, click "allow other network users..." and then choose from the list (if there is a list) which adapter is your "local network" or whatever.