Hello Benjamin Haines,
In my experience, I'd say it is a display issue. It sounds like LCD/Digitizer is defective from the fall, but there is always a chance of something coming loose.
If you have not already, try and open up the phone and remove the screen assembly. Then take a q-tip and some rubbing alcohol to clean the ribbon connectors. Allow time to dry. After reseating the cables, try and turn it on. If this does not work, you should try replacing the the display assembly.
*Know that sometimes the logic board can become damaged from drops depending on how severe.
I hope this helps you in fixing the iPhone.