Why is my display not working

Generally the fact that your external monitor works is a good indication that your graphics subsystem is working correctly and that you're most likely looking at a display hardware failure.

Based on your description it seems likely either your LCD or your backlight has failed. You can tell the difference by holding a flashlight up against the screen in a darkened room and seeing if you can make out a picture.

If you see a picture then there are a few possibilities; it could be a fuse on the motherboard, or on older models that use florescent bulbs the driver circuit may have failed, or you could simply have a flex cable or wire next to the hinge that's broken over time.

Otherwise you may be looking at a dead LCD screen. Those can be replaced without too much pain; the hardware maintenance manual on your laptop's device page gives detailed instructions on how to remove and replace it.

V1415 G2 Hmm - iFixit

So take a good look at the screen and see if you can figure out whether it's the backlight or not, then come on back and let us know what you found. Once we know that, we can help you figure out what your next steps should be.