At the moment, the wireless adapter isn't getting its IP address from the router, hence the "Limited
or No Connectivity" indication.
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 adapter should get its correct IP address by DHCP from the router.