Before trying the following : Ensure if disabling source of power to remote or main control panel if they need re-linking and that you know how to do it.
Doing this is a pain in the butt however it may save you money.
Try the following remove the remote batteries change for new batteries then see if this stops the door opening. If so job done.
If the door still opens with batteries in or out of remote then the fault must be in the control panel. Isolate the power to the control panel for 15-30 minutes. (look for a reset button if it had one).
Usually some electronics get confused and removing and restoring power usually resets and stops them messing with your brain.
My roll shutter garage door control went on the blink and the company who fitted it yrs before wanted £400 for new remote including call out charge. Its now on a key operated secure switch the motor is a mains power one so if you change yours you must ensure its a mains motor most are but you need to get it checked out.
bob
February 2013