Though difficult to diagnose or give suggestions without being able to inspect it, I would first do what you have done...open it and unplug battery before starting. Then attempt to reseat the connectors. 2nd I would try a hard reset by holding the home and power buttons down for 10 seconds or so to reboot. Connect to iTunes and do a backup, in case you lose power, or some other issue occurs so you don't lose data. Maybe even doing #3 first....
Does your flash or flashlight still work?
It could be a hardware issue where a component has broken a solder joint and would need microsoldering done.
You could even restore your phone to see if it is software, but doubt it since the symptoms began after a drop.
If none of the above work, you could try to find a micro soldering shop close to you locally or look through the pros here on iFixit and you may be able to find someone where you can mail the phone in for repair at a reasonable cost most don't charge if the repairs unsuccessful so you have nothing to lose that way