The screen only lit up when it was open to a 45 degree angle. It was on at other angles, but it was dark, no backlight. Google said it was probably an inverter cable... then, ta-da, I found this site.
42 steps and back again. Took 2.5 hours (I'm a bit slow). I meticulously organized the screws when they came out, and laid them out on a piece of paper with the step number beside them. Process worked well. And the problem was fixed with the new cable!
Be patient. If an odd shaped part comes out (like some metal pieces near the hinges) or if there is an extra cable, or a specific wire routing, there is nothing wrong with taking a quick picture yourself with your phone, to consult later.