The Wireless Network Adapter has been unable to get an IP address (probably in a 192.168.x.x range) from the router and Windows has defaulted to allocating a 169.254.x.x address. This will give the "Limited or No Connectivity" indication and the Laptop will be unable to access either the router or the internet.
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? You should be prompted to enter any WEP or WPA encryption key and, once "Connected", the wireless adapter should get its IP address by DHCP from the router and you should have network and internet access.
There is a difference between the Wireless Network Adapter and Router communicating with a good signal and "Connecting" (as in "logging in") to your Wireless network.