There appears to be a damaged inductor (PL10) in the first image, approximately 25% of the outer package is missing which includes one of the inductor terminals.
There is also what appears to me smoke residue deposited on the PCB, emanating from the area just below PL10,PL11 and extending downwards.
The loss of PL10 is certainly a contributing issue to the main problem, however there maybe other damaged components present, which are not detectable from sight alone.
It would also be prudent to test the condition of the charger/power supply pack, as it may have been damaged as well.
BigDog