Hey there. It definitely sounds like the LCD is busted from the fall.
You can try opening it up and disconnecting the screen cable and reconnecting to see if that works, but if not, I would recommend replacing it. The replacement guide linked here will bring you to where you can do this, but also if you need to put on a new screen as well.
I don't know what carrier you are using, but this link is basically the part that you need. Here on iFixit, they only have the full assembly for the Sprint model. You can always check Amazon or Ebay if that's not what you're using though.
If you don't want to rush into replacing the screen and you have data backed up, here are a few steps you can take to reset the phone: (source)
Hardware factory reset:
-Take your phone and turn it off – just press power button and select “power off”.
Wait while your device is shutting down.
-Then, press volume down button and power button together until the LG logo appears on the screen.
-When the LG logo is displayed, let go of the power button, keep pressing the volume down key and then press once more the power button.
-Once you do that, on your LG G2 the factory reset menu will be displayed.
-Press power button in order to agree and wait while the hard reset is being completed.
Software factory reset:
If you can use your phone then you can perform the hard reset in an easier way.
-All you have to do is to tap on the “menu” icon.
-Go to “settings”.
-Select “general” and pick “backup and factory reset”.
-Then choose “factory reset”, agree and complete the hard reset operation.
If all of these options do not work, it could be board damage, but it definitely is worth it to open the phone to check everything out.