Here are some photos inside the mysterious gray strip.
Unfortunately in my case SQUEEZING did not solve the problem. It is annoying because if I squeeze or especially bang it, it will "flick" to being correct for a few moments. But then it falls back to the dim state. It's easy to assume that something is simply loose. So I thought, can I get inside the **** LG LED unit??
Let's see! Notice the piece of scotch tape, which is pointless - rip it off.
Here are the six enormous images: http://postimage.org/gallery/toakbhq/
That site is very useful for posting large images. Click on an image, and click again for the enormous image where you can easily see individual pixels on the running mac screen, etc.
Here is the mysterious black strip. Rip it off. Underneath is mysterious slots.
What is inside the mysterious slots?
Unfortunately I do not know and couldn't find out, but it must have something to do with the backlights. I shoved every sort of tool inside all of the slots, I used a hammer and chisel and so on. (You can see the marks in the hires photo.) Unfortunately as I say I could only make it "flick" to the correct lighting -- I was unfortuantely not able to get a permanent fix by applying pressure.
Note that WITHOUT disconnecting the four cables that connect the LED unit, you CAN carefuly edge out the LED unit, and, sit it on top of the frame - you can get your hands under all four sides at the same time. So the mac will still be running normally with the screen hanging out. A small point, don't forget to thread just the power cable on the back of the machine "not" through the elegant stand hole, so that it does not foul the stand when the machine is lying down. By the way in this photo you can clearly see the problem where half the screen is dim.
To be clear just unscrew the eight simple screws which stop the screen from tumbling out. Then lift out one edge of the screen. LOOK UNDERNEATH AT THE FOUR CABLES, to see how much play you have (you can only lift it a few inches. Then pull it towards you an inch, and then the other edge of the screen will slip out. Then you can lift all four edges and sit it on the iMac case like this.
So I could not achieve anything other than a "blink" fix by squeezing or beating on the LED unit. Next I tried to remove the piece of metal that wraps around the screen. Notice you can see TWO screwholes on the relevant piece of metal here (one pointing left one right), there are two more at the top. I unscrewed them, but unfortunately, the piece of metal does not come off in any way I could get it to come off. (I don't know if it's due to adhesive or what - I used chisels, heavy pliers, roofing tools etc and it would not budge.)
Continued ...