Take it apart and look for damage! It seems most likely that a bit of solder between the circuit board and the cable receiver cracked, so that it doesn't make a connection when the cable is at a certain angle. It may also be a wire in the cable is crimped or damaged. Then, of course, it could be be where the wire connects to the LCD panel. All of these could be repaired with a low-wattage soldering iron. The real trick is finding the culprit.
If it's not visible, perhaps a multimeter will expose the fault.
Plan on spending a few hours on this project, and a fair amount of patience. You will probably also want a working computer with internet in case you need to look something up.