The L4 coil supplies the voltage to the backlight of the screen, the voltage comes from the adapter or the battery through a transistor to the whole motherboard, it is called B+. Somewhere a trace is open or you have a bad solder, this is why you have no voltage to the coil. You must follow the B + (about 19 volts) to see where you lost the voltage, it should be around the coil L4 because everything else of the motherboard gets the power.