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 little icon will get its "halo" to indicate it is connected to that network and it should then get its correct IP address by DHCP from the router.
Note: When setting up third-party wireless adapters with Wanadoo's Livebox, you have to set it to "pairing" mode. Follow the instructions in their tutorial at click here