Chosen Solution
This happened in a 21.5 mid 2011 iMac. I damaged the LCD thermal sensor socket in the logic board. Now the connector won’t stay in place. I know the missing thermal sensor should cause the fans to spin up (they do spin up after a while), but the screen is blank. I connected an external monitor and it works fine, so it doesn’t seem to be a graphics or logic board issue. I replaced the LCD panel and the LED driver board with ones from a working iMac, to no effect. Can the disconnected LCD thermal sensor cause this?
Update 2020/02/06, added pictures:
LVDS socket:
LVDS co9nnector:
Broken thermal sensor socket:
I would look at the logic board LVDS connector and the cable. I’m suspecting one or both is damaged. Take some pics of the connector straight down, from the front and side as well as the pin side of the cable (original displays), post them here for us to see Adding images to an existing question Update (02/06/2020) Sadly you do have a bit of bowing in the logic board connector, so it was stressed. We can also see the corner of the cable is damaged as well. As far as the sensor socket it too is damaged ;-{ At the point I think its best to find someone with the needed skills to replace the connectors. This is beyond what even I can do these days.