Garage doors open with the remote control or keypad, wall button switch or manually. When all efforts are exhausted and the garage door won't open, chances are there is a problem with either of these parts. It's simpler to start eliminating them one by one. One must try first to use the clicker and if the door it's stuck on the floor, the wall button must be pressed. If the door still doesn't open, the problem is found in the main opener unit and will relate with either the motor or the reverse mechanism.
Another reason for garage doors refusing to open is broken garage door springs. If you try to open the door manually after unplugging and disconnecting the electric opener and the door doesn't move, it's probably due to broken springs. In this case they must be replaced as soon as possible and by a professional, as it is a very dangerous repair for one to do on his own. This problem is rather serious but there might also be a simple explanation, too. For example, if the opener hums but the door doesn't move, it might be too much snow preventing the door from opening.