Broken cable is not common unless there is physical damage. Besides the cable, there are 3 parts involved: the motherboard, the panel and the Hall sensor (lid closed sensor). I have not worked on that model so I am not sure where the parts are located. Motherboard problems are usually related to the fuse, but they don't blow for no reason. They are easy to blow while you are working on things, especially plugging and unplugging cables or screens. The fuses are usually very near the LCD connector. Most of the little parts on a motherboard are fuses, capacitors and resistors. On most machines the resistors are black; the capacitors are mostly brown, and the fuses are often white with metal bands at the end and maybe a single letter on top, denoting the capacity. You can test the fuses for open circuit with a meter, but if a fuse just blew out, there must be another underlying problem. The Hall sensor as a magnetic switch that occasionally fails. On most models, there is a little magnet in the palmrest that trips a switch in the lid (often on the side or near the microphone and camera). When you close the lid, the switch gets near the magnet and the backlight shuts off. I try to figure out where they are by sliding a little screw around on the palmrest until the screw jumps to the magnet.
Were you doing anything when the backlight stopped working?