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This is old enough that it could have had a screen replacement already, so put a magnet by the battery indicator. If it dims the screen, then someone popped the magnet out and didn't put it back while replacing the screen.
If that doesn't do it, check SMC_LID on the board when you put the magnet there. If it lowers, then it's a board issue, if it does not lower, then it is a battery indicator/sleep sensor issue.