I had an electrically operated garage door in my last house. Can't remember the make but I suspect they all operate in a similar fashion. Find the motor housing, which is usually at end of the chain track above the middle of the door. Switch the electricity supply off. On the housing there should be a coloured (usually red) plastic knob maybe with a cord or chain, if you pull this it should disengage the motor form the chain pulley and allow you to operate the door manually. This is there in case of a power or fob failure. Maybe a check online at YouTube or the makers website will assist. Good luck.

Concrete

I'm wondering if its just the button that has 'failed', possibly due to build up of dirt/dust between the button contact and circuit board. I had this problem with a remote control for my DVD player, and so, following the instructions from a video on YouTube, I opened the remote up, took the rubber botton tray off and cleaner it (the side facing the PCB) and the PCB contacts with car electrical contac spray cleaner (onto cotton buds) as I couldn't easily source any isopropyl alcohol in small quantities.

Lo and behold, after a bit of fiddling to get the control pad open, it now works as new again, admitedly with a few scratches in getting the plastic halves apart by prising them open. Not sure if you could attempt something similar - perhaps someone more qualified than myself on electricals may want to chime in with an opinion.

Might be worth a trip to the local Timpsons to see if they can repair it.