Inspiron 1525 WiFi shows connected in 'Connect to' panel but Network icon in system tray is not on and won't connect to internet

I bought my Granddaughter a Inspiron 1525 in March 2009 with Vista Home Premium O/S. The wireless connection worked fine until 2 months ago. They have a Netgear router 'G' setup. When you look in the  panel in the Start menu it shows the home network is connected but the network icon in the system tray is 'X'ed and will not connect to the internet. I have turned the wireless slide switch on the laptop off and on, disconnected the network connection in the 'connect to' start menu and clicked on 'connect to' to set the connection back up, unplugged and reset the router. but still cannot connect to the internet. Does anyone have any suggestions what I might try to do to get the internet connection working again?