If the phone is not heating up then u probably need a battery replacement and after the replacement if it still doesn't charge,check your charger and your charging port. Try cleaning the port with alcohol (spirit) with toothbrush. If still go for complete replacement
Check your modem firmware. Go to settings,general and about and check if there are numbers there,if no numbers it means firmware is corrupted. First restore your phone and if still problem not solved then you go the hardware way. You'd have to change your base band chip which is a bit difficult.