Sometimes after a drop, or after repeated drops, the logic board can be damaged, specifically the solder connections underneath some of the IC's. This can affect pretty much any IC and it can cause some unpredictable symptoms.
However, before getting into potential micro-soldering repairs, you need to eliminate the possibility that there is a problem at the modular level. [guide|57073|Open up the device] and insure that the battery is properly connected, as is the screen assembly. If you have access to another, preferably known-good battery or screen...or even a Lightning port flex, try those too.
If that doesn't solve the problem, then your charge circuit on the logic board is damaged and will require a micro-soldering repair.