The USB wifi connector is only for use when you don't have a wifi router (it plugs into a PC and acts as a point-to-point wireless access for the DS).
There should be two things governing access to your router -
the DS only has a 'B' wireless card and will only support (the very insecure) WEP security. If your router is setup for either WPA (highly recommended) or operates in pure 'G' mode the DS will not be able to connect.
If you are able to check the Wireless sceurity settings, try temporarily dropping it to WEP and then firing up the DS. (Note - any other existing devices will lose their connection!)
Have you checked out the official
DS Wifi site?