IIRC those models were prone to graphics chip issues, like separation from the logicboard. I think the trick to fixing them is to place a nickel on top of the graphics chip and when you put the machine back together, the coin will press the chip down and restore it's connection.
Here's one thread on the issue:
https://forums.macrumors.com/threads/611881/
That's just one possible issue. Have you tried connecting an external monitor? If that works, then it's an internal cable or backlight or inverter issue. If the external monitor doesn't work, it's something with the graphics chip itself.