Try a proxy server called proxyi .
My friend has AOL DSL and can only access AOL through each computer when that specific computer logs into AOL through the AOL dialer, regardless that we are on a wired router.
Essentially, once you log one of the computers into the AOL connection, you will be using that computer as a "middleman" to access the internet via AOL.
Please note that he has a US version Wii, but we are in Europe, and can access every Wii channel except for the Wii shop, because it is apparently region encoded. I'm trying to find a way to spoof the IP address to make it work, and ran across your question.
If you're using the correct version for your region, hopefully this will help.
The proxy server is very easy to use, just install it, and click "ok" or whatever in the configurations menu that appears (making sure you are connected to AOL).
Then, on the Wii, go into internet settings, tell it to use a proxy, and enter the IP address of the computer using the proxy, with the port number 6588