Found the solution… the little clamping mechanism that should be opened before pushing the flat cables back into the connectors on the motherboard. Without doing that, the cable does not slip in far enough and as a result the display stays dark. Maybe worth an update? Thanks!

I had a big black area on the screen and replaced it with a new one. I did exactly what was described here, but now the new display just stays dark, like it would not get any power. Rest of the cam still works fine. The copper clamp is there to give the display grounding connection. Then put in the old display again and that one now also stays black. Any idea what I could do or check?