Some thing simple with the flex cables for the keyboard/touch pad may have been shaken or pulled lose in the falls. Not a complete disconnect but enough to cause a difference in the amount of electricity it takes to send the signal through. An IC, resistor, cap, diode, or something else might have been damaged on your motherboard.
WARRING do not do this unless you are sure you can do it or laptop stops working.
If this is not one of those unrepairable ultra books I would try to find an diss-assembly guide online. If you think you are up to it study the guide until you are able to memorize it. Then disassemble to the point of taking off the palm rest. Inspect the flex cables, the connectors on the touch pad, and the motherboard. If it is easily done at this time and you have thermal compound it would be a great time to clean the heat sink fins. Have come across a lot of laptops that the air flow is blocked by what looks like felt covering the fan side of the heat sinks. Just be sure to remove all sources of power before doing anything else. It is also good to ground yourself. WARRING do not do this unless you are sure you can do it or laptop stops working.
If you find you need to replace parts Ebay is usually the most cost efficient place to find them. Although as you laptop is newer you may not be able to find many parts on Ebay. Search by the laptop model number and the individual parts number. All of my laptops have been bought broken and then fixed by me.