If the Wireless Network Adapter is unable to access the router and get its IP address, Windows will default to allocating an APIPA address (Automatic Private IP Addressing) in the 169.254.x.x range. This will give the Limited or No Connectivity indication and won't let you get online.
Try going through the procedure to "Connect" again to the Wireless Network, i.e. run the wireless adapter's software, scan for "Available Wireless Networks", find and highlight the one that matches your router's SSID (network name) and select 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.