Despite the WiFi connection sign you may not really be connected to your WiFi network.
Your BTFon router may not have given your iPhone a valid IP address when the iPhone requested it. To check on this go to the Settings App (Settings > Wifi > your network name) and touch the ">" to the right to see the network details. If the IP address shown starts with 169 or is blank then your router didn't provide an IP address and you won't be able to access the Internet.
Sometimes the fix for this can be as simple as restarting your WiFi router (remove power to it for 30 seconds and restart). Next, reset network settings on your iPhone (Settings > General > Reset > Reset network settings) and then attempt to connect. In other cases it might be necessary to update the router's firmware with the latest from the manufacturer's support web pages.
If you need more help please give more details on your network, i.e., your router make, model and version, the wifi security being used (WEP, WPA, WPA2), etc.