It appears that it's a general problem where users can't turn off the Flight mode on their Nokia phones running Windows. Here are some things you can try to turn off Flight mode, based on users experiences:
Factory Reset the phone. It will wipe the settings and you'll have to go through the initial configuration as well.
Use the Windows Phone Recovery Tool and flash the firmware again. it will wipe the phone as well.
Take the phone to Nokia Care and they should fix it for you.
Visit a local phone shop and they will attempt a possible fix as well using firmware flashing or direct system access.