Gets hot when plugged into charger

My phone has been working like new but recently dropped from about waist height while inside a durable case. No visible damage but it completely shut off. When I tried to charge it, it got hot. I took it to Apple and they tried replacing the battery but said it wasn't the issue and that I may have to replace the entire back panel and suggested it might be a logic board issue due to the heat when trying to charge.

Does anyone have any clue to think the logic board is fried and unfixable?