<<< a pop up says little or no connectivity >>>
That suggests that the wireless adapter hasn't been able to get its IP address from the router and Windows has allocated an address in the 169.254.x.x range, which won't let you get online.
Have you actually "connected" to the router? If you run the adapter's software, the Site Monitor should look for "Available Networks" to connect to. When it finds the one with the SSID (network name) that matches your router's, you "connect" to that network and the little icon should then get a "halo" to show that it has connected.