It is also possible that after tapping on the LCD lid close switch the backlight works fine, you see a normal video on the screen for some time and then the backlight turns itself off again. In this case I would blame the FL inverter board. Try to reseat cables on both end of the FL inverter to make a better contact between the cables and the FL inverter board. If it doesn’t help I would try to replace the FL inverter board.
If you see the same garbled video output on the external monitor most likely it is not the LCD screen problem. In this case the system board (with onboard video) is bad or the video card is bad.