Answer to "The LED light on my Camera won’t turn on."The camera's front LED light might have blown a fuse if on for an extended period of time. Also the light might not be fully touching the connections where it is attached to an internal circuit board. This would cause a break in the circuit that provides it with electricity and therefore it would not work. Also as Jeffrey said, it might be on but it could just be dirty.
Answer to "Why won’t my camera turn on?"If the camera itself is not turning on the first cause would be a problem with the battery. If the battery is not charged it might cause the camera to turn on but if it is charged then it could be a dead cell on the battery or a missed connection from the battery to the camera.
Answer to "Why won’t the screen on my camera turn on?"If the internal screen will not turn on there is a chance there is a faulty connection either to the battery or to the input of the screen from the camera. Of course it could also just be the screen itself that is broken or cracked. To correct this you will have to check the connections to the screen and if that is not it a full replacement might be in order.