I think that I got the problem now!
The Wii can find the access point (the connection to the wireless network card). BUT when Wii is testing the connection it's testing the "internet connection" - and there is non on the wireless network!
The internet connection is on the non-wireless network card and comes from the router.
So the thing is - how can I make the wireless network card internet able, forwarding the internet connection from the non-wireless to the wireless to the Wii....