So, does the Internet work on the wii when it doesn’t work on the computer. Or do both not work? If both dont work then its the router, I had the same problem, after a while I had to reconnect the router like u said; so that it would work again. I went to my routers website, and downloaded the latest firmware for my router And now it works fine. Try going to the website from the makers of the router, they should have a help page.