You've done some great troubleshooting to identify the problem. The only other useful information would be to know the exact model of the Mac which can be found by clicking the Apple menu and selecting "About This Mac".
If you have a USB-C model Apple laptop, then this is unfortunately a very common issue. Sometimes you can close the lid and very slowly open the display so that you can see video on the built-in display, but after opening the display about 45 degrees the backlight will go out (sometimes it is possible to very slowly open it past this point and keep the screen on though it is rare).
If you have the MBPro 13" (2016) model, then Apple has a free backlight repair program for this issue. Unfortunately any USB-C Mac has the potential to experience this problem, but only the 13" 2016 model is covered by a free repair.
https://support.apple.com/13-inch-macbook-pro-display-backlight-service
FYI, here is a current list of the publicly acknowledged free repair programs for various Apple products (some have multiple programs):
https://support.apple.com/service-programs
If this is a personal laptop or an older pre-2016 model, then you will need to have Apple or an Apple Authorized Service Provider examine the laptop and provide a repair estimate.
If this is school provided laptop, then contact the school for support so that they can provide you with another laptop to use. Even if this is a personal laptop you can still contact the school to see if the school can provide you with a laptop to use while your personal laptop is being repaired. Or you can use the laptop with the external display until a more convenient time to repair the laptop or until the school can provide you with a loaner although you may need a USB camera if the built-in camera is not be working.
Good luck.
