I had the same problem with my daughter's machine. The solution was to select "connect even if the modem is not broadcasting" AND "Start this connection automatically". That seemed to solve the problem.
Hiding the SSID just makes the wireless router not shout it's name to all and sundry, the SSID can still be discovered by other network tools.
You should also have set-up encryption - ideally WPA2 but if not WPA, avoid WEP.
You should set up the router to limit access to your router to known mac addresses.
Good luck