As shakalnokturn said, it is probably LED failure. You can measure ouput voltage (if I read correctly from picture it is marked +VLED and -VLED). Measure with backlight connector connected and then disconnected. If the voltages measured are very similar, that probably means that the LED strip is open circuit (could also be PSU failure, but unlikely). If the voltage is zero then it means PSU failed, LED strip is shorted or it could be a fuse (I see a fuse in the picture, presumably for backlight power output, small rectangular soldered on the board).
Hope this helps to get started, but be careful of high voltages and don't harm yourself. Backlight voltage could be quite high, not to mention the main bulk capacitor of the PSU.