Have you actually "Connected" to the wireless network? In other words, have you run the wireless adapter's software, scanned for "Available Wireless Networks", found and highlighted the one that matches your router's SSID (network name) and selected the option to "Connect" to it? Once "Connected", the wireless adapter should get its IP address by DHCP from the router and you should have network and internet access.
At the moment, your wireless adapter has failed to get its IP address from the router and Windows has allocated a default 169.254.x.x address. This will give you the "Limited or No Connectivity" indication and you will be unable to access the network/internet.
There is a difference between the adapter and router finding each other and "Connecting" (as in logging in) to the Wireless Network.