I'm not familiar with your exact car but here is something to try. Allow yourself a couple of hours in dry weather as the door will need to open for a while.
I would take off the handles etc. and door trim panel on the back door,
*carefully* remove the plastic sheet (you will need to put it back later with waterproof adhesive tape) and have a look at the door lock unit. There should be two wires running to it. If you can disconnect the unit (there might be a plug and socket in the door) try a 12V transformer (or a spare 12V battery) with a couple of wires to try to operate it manually. Reverse the polarity of the wires to activate/deactivate the lock unit.If it doesn't work, then replace the unit. If it does work, check the wires as they pass through the door pillar into the door, they may have become damaged and you will need to replace them. Easy to do this with a couple of wires and some scotch clips. Make sure the rubber grommet is in place to protect the new wires.
Since you described the normal operation of the other doors, it has to be a localised fault at that particular door.
I used a similar method to this to locate the fault in an Audi 80 powerlock system.
Hope this helps.
If not, post again and describe in detail what happened and I'll think of something else.
Keith