Update (2018/09) My display is still up and running after changing the Capacitors, but I reckon this is only coinsidense. I would advice you to have a look at James Stuart comment/explanation below. I think it makes the most sense and explains the cause of the problem well!
If the display is not even recognized by the system, I would try listening if even the fan starts to roll. Otherwise I would go further checking the power voltages first. But yeah as @SW said You might as well quick try and see the Panel with a flashlight if you have a weak image without background lighting.
I would guess that if the display is not connected to the laptop video output the display shutsdown/ power save mode => switch off the LCD voltages => I havent checked the TP11 but I guess it goes to the LCD or LEDs. if you read the issue: What components need replacing on the Logic board? You will find an an extensive description on the LED background not lighting. If you have any questions just ask and I ll see what I can find out but please read the thread carefully, I think you ll find your answer there.
Ich habe das gleiche problem gemerkt und dann habe ich in service manual gesehen das der verursache war falsch versteckte sensoren im Logic board. Der display temp sensor und der andere blower sensor sind vermutlich verkehrt.