You could buy a crossover cable and plug the Wii into your computer, then set up a bridged connection. You do have more than one ethernet jack on the computer, right?
You may just be able to use Internet Connection Sharing in Windows, but I'm not entirely sure. I've only used that for using a laptop's wi-fi on a desktop without it.
Nah, a crossover cable is just a special type of ethernet cable. Just take a peek at this. It's for the 360, but should still work with the Wii.
So wait. You don't have a router. Or a wireless router. You tried to use internet connection sharing with the Wii. How did you have the Wii plugged into the internet when you were doing this if you don't have a second ethernet port? Are you using some goofy USB satellite internet dongle?
Oh man, I never knew you could pull half the shit done on this. Granted its tool assisted, but there are probably one or two things you could manage once during a race.
hah, clever. is it some sort of speedrun?