I’ve had the same problem on a 2009 27” Quad Core i7 iMac. (1) The display comes on but the backlight will not stay illuminated unless set to a lower setting (+3 on the scale). (2) I have found that when the light nears going off, the 3.3 volts coming from the Logic Board to the backlight inverter board has sagged to 2.9 volts and suddenly drops to 2.7 volts when the backlight goes off. (3) When the backlight has failed, I can use keyboard commands to make it sleep and then reawaken, but the backlight will not stay illuminated unless set to the lower illumination setting of +3 or less. (4) I have found that if the computer is unplugged overnight, the display will run at full illumination for about four hours before the faulty behavior begins to occur again. (5) I have read elsewhere that the 3.3 volt signal to the backlight board is what commands power to the backlight or turns it off. This voltage is supposedly generated by the Video Card. (6) Others have claimed they have severed this connections and...

Exact same problem, which happened after a HDD replacement to SSD on a late 2009 iMac. I salvaged the circuit board from the old drive to keep the HDD temp sensor in the circuit to control the fan speed.  The display blackout started almost immediately after replacement.  I replaced the LCD temp sensor but to no avail. I wonder if the apple built-in diagnostic process looks for a delta between the various temp sensors and shuts down the display if there is too wide a disparity between them? Thinking of trying the inline digital thermal sensor cable from OWC.

Exact same problem on a 27” 2009 iMac. I use the same workaround of keyboard strokes to force the display asleep and then wake with another keystroke. The screen runs OK for very long periods at low light settings and is more prone to failure when set at mid to higher light settings. I replaced the inverter board with a used one but the problem got much worse!! I could hardly keep the display illuminated for a second before it went black at any light settings. Electrolytic capacitors on the inverter board might be the culprit. Caps are notorious for failing with age. I see four large electrolytic caps on my board. Perhaps I should acquire some spares and see if that fixes the problem. Anyone had success fixing this issue?