If that's correct and it still won't connect, try toggling on "Airplane mode", which will turn off the cell antenna, as well as WiFi. Then try turning WiFi back on (with Airplane mode still on) and try to browse the web again. That should eliminate any possibility that the phone was trying to communicate via cellular network instead of WiFi (it should automatically default to WiFi connectivity if there is no cell network, but maybe there is some glitch with that?).

If none of that works, then I have no idea what to suggest. Maybe try connecting to another wireless network to eliminate the chance that maybe the phone just doesn't like your wireless router?