You are going to have to try and force it to turn off, or wait until your battery runs out (unplug charger). There is no short cut really to turn it off in this case. Also, you are going to have to test it to see if it is the laptop or the display that is the problem (once you can get it turned off).
1. Turn the laptop off.
2. Connect an external monitor to the device.
3. Turn on the external monitor.
4. Turn on the laptop.
Can you see anything on the external screen? If yes, then the attached display is the issue. You would need to first check the ribbon cable that connects the display and if that is not loose, damaged, pinched, etc., then the display may need replacing.
If, however, you can't see anything on the external monitor either, then your graphics card/GPU is probably toast, which means you may need to replace the motherboard.
NOTE: If you laptop is still under warranty, make sure you contact the manufacturer about a repair or replacement rather than opening it up yourself and voiding your warranty.