First, from you description (that's all I have to go on), this was caused by SOMETHING that happened when you dropped the unit.
The fact is you could have done a lot of serious things that are not apparent (and that the local "hospital" can't fix). FOR EXAMPLE, you may have "cracked" either a circuit board trace or a solder joint that is usually in position and touching anyway (hence making electrical contact, hence working), but it is, in fact, no longer one piece, there is a "crack" in what is supposed to be a solid conductor of copper or solder, and the laptop is, thus, consequently now "flakey". If that had happened (it could have, but I'm not presuming that it did), the only fix might well be to replace the motherboard, which probably cannot be done economically (in other words ... the fix is to buy a new computer).
Less seriously, a connection (one that can be reseated, such as the keyboard to motherboard cable) may have been knocked loose. That could be fixed.
But I think, from your description, the most likely cause (not the only one) is that when you dropped the unit you damaged, but did not destroy, the hard drive. So, now, when the unit tries to access the hard drive (and, likely, only certain spots on the hard drive), it "hangs" and other things (like responding to your keyboard keys) come to a halt until the hard drive resolves things (or declares failure and gives up). By no means is this the only possible cause, but I do think it's among the more likely causes. Although there may be ways to "repair" the hard drive, my preference would be to try a different drive (not touching the current drive in any manner at all) and see if the problem goes away. For testing (to see if this is the problem), if you don't have a spare hard drive, you can probably find a used but good SATA 2.5" hard drive for $20 to $40. That is the first thing that I would try if this was my unit.