Have you tried looking at the Sharing preferences in the System Preferences (under the apple menu in the upper left corner)?
There are three tabs: Service, Firewall, Internet. Choose the Internet tab.
You can select the "Built-in Ethernet" to share
from your computer, and also check the "Built-in Ethernet" in the list below to share
to other computers, and then start sharing. Since you said your Nintendo Wii has ethernet, just connect your computer to the Wii with an ethernet cable. (It does not have to be a crossover ethernet cable, it can be any ethernet cable, your PowerBook G4 will figure out that part.)
I haven't tired it with the Wii, but I have tried it to share an internet connection from my PowerBook G3 (Pismo) to an MS Windows XP computer a couple of years ago and it worked well. If you have issues connecting to the internet with the Wii, you might consider turning off the Firewall to see if that helps. Hopefully you won't have to turn it off, but if you do then maybe you can figure out what ports you have to open so you can add them to the Firewall list.