Chosen Solution
As soon I open my display more the 90 degrees, I got a black screen. Not totally black because I can still see the content very darkly. When I move the display to 45 degrees and back to 90 degrees it is ok again. Anyway 90 degrees is very uncomfortable. Is it perhaps a cable break of the power cable to the display? …or what can it be? How exactly can I repair it and where do a find a manual for it?
Your inverter cable is broken internally. You need to replace it. Instructions for replacement are in this guide. There are 2 different inverter cables for the A1181 MacBook one is referred to as 4 walls the other as 3 walls. Here is a video that does a good job of explaining the difference between the 3 walls & 4 walls. I would use part of the fore mentioned guide to remove the upper case/keyboard to get a visual as to which cable is used in your MacBook. I would buy a new one if possible. If you buy a used one, buy from a reputable seller that puts a warranty on the part. Here is a google search to help you find your part.