It’s possible that when the computer fell, it partially unseated one or more of the display cables/antennas inside. You can try to reseat the display cables and see if that resolves the issue. If not, chances are yes, you’ll need a full display replacement.
By the way, just so you’re not wondering “Who the hell is this random ass dude telling me what to do?” I’m an ACMT/ACIT certified technician working for an Apple-Authorized service provider (AASP), and we’re actually held to higher standards than the Apple store, so I can confidently say I kinda know a little something.