Chosen Solution
Small spill, shortly after, backlight died for good. Apple says it needs a new logic board. Inverter board sounds more likely to me, but I can’t even find reference to one in this machine. Is it built into the log board?
It is built into the display. Unfortunately, a liquid spill is most likely to damage the logic board. One way to check is to remove the upper case and look for corrosion on the board, especially near the keyboard and speaker area.
There definitely isn’t a board just for the inverter but you could try replacing the inverter cable itself. After a liquid spill, it would be natural of Apple to assume the logic board but if the backlight is the only problem, that seems unlikely at best. I would try replacing the inverter cable, followed by the display. Only then would I try the logic board.
Take a look at the post below, which has some more potentially useful info. no display backlight
