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...than why does it say I'm connected on my computer!?!?!?!
Temporarily disable your firewall and see if it still persists. That seems to make me think that it can connect to the computer through the dongle but the computer is stopping the Wii from then connecting to the Internet.
If that doesn't work, clear everything and start afresh.
1. Uninstall the WiFi dongle software (this is the stuff I can't help you with setting up). Clear the wireless settings in your Wii.
2. Install the WiFi dongle software. Disable (temporarily) the firewall you have running (Windows Firewall or something else?)
3. Set up the Wii wireless connection and perform the connection test.
4. Once you have that working, permit access to the WiFi software on your computer (can't help you with specifics but I think that is where the problem lies).