When I open the lid of my laptop more less than 90 degree, screen and back-light works fine. When the lid is open more than 90 degree, screen works fine but back-light turns off. All other components of the laptop works fine. The problem has started only recently, and the laptop in question is a Lenovo G510 and is out of warranty.
I have the same problem with same model. At least MY problem is because of poor design from lenovo, The hinge (Left one) that leads the wires, have managed to internally break one of my backlight wires, so I have to push hard down on the hinge, or adjust the screen's rotation. See if that also goes for you. Push hard (not too hard so that is possible breaks) to see if the backlight lights up, If so you may have the same problem.