I have bought an entire screen assembly and everything has worked again. So I concluded that the old LCD screen was the cause. The old LCD was replaced by the new one and my assumption was right and the backlight issue has been solved! But be aware of the right model number ;-)
after closing and opening the display the backlight will come back for less than a second. unfortunately i have to wait about 2 weeks for the new inverter cable... I will post here again when I replaced it. thanks again for your help guys!