I just connected my Wii for the first time today and I to had the same problem as you. I tried my connectection test numerous times without success.
I don't know if you are getting any error codes (I myself got EC 51330). If you did I suggest going to http://support.nintendo.com and looking up the error code. Nintendo has a great support service as I had to use it alot today.
Heres a few links that helped me when I was having problems:
Error Codes - http://www.nintendo.com/consumer/sys...rors/index.jsp
Router Compatibility -
Connecting Support -
Connecting Walkthrough -
Hope these links help man. I think (don't quote me on this) but I am pretty sure that most if not all the problems you have can be solved by a bit of surfing around on that site.
As for some advice of my own, it could be your router settings. Turns out all I had to do was enter a MAC addresss to mine and it worked.
Hope you get an easy fix,