Are you positively sure the rear jacks worked right until you dropped the remote? Or was that data point days or weeks ago and the problem could be with the control board, wiring, or fuses and just appear to be connected to the drop event. If not...
Did you just drop it on the ground, or in water?
Will it work with the cable attached (probably not)?
Aside from replacing the remote, I know of no surefire way to repair it... But once you have a replacement lined up, there is no harm in disassembling the old remote before you order a new one. I would think there is a crack somewhere in the board or a defective soldering jount. Carefully taking a heat gun to the board *might* work. Maybe you can find a small local shop who (still) does repairs.
These things are pretty rugged. I would expect a minor mechanical cause. Just how to find it...