black LCD can be one of two thing. 1. LCD leakage or 2. Backlight bulbs are dead.
if whatever in the LCD display is leaking, there's not much choice. I would suggest to get whole A/C control unit replacement from ebay or junk yard.
you turn off the engine (and lights) and if you still see black LCD screen, then it's more likely bad LCD display. Those screen gets worse when it's cold. when it gets warm, the dark spot would be gone.
if it's caused by the bad backlight bulbs, you can replace the bulb but you need some soldering skill.
our A/C backlight has 3 bulbs (left, center, right). You can tell if you have dead bulbs by turn off the light. if your display is fine (no dark spot) then you have dead backlight bulbs. you can change the bulbs yourself but you can't get those bulbs from the dealers.
