Attempt manually turning on the phone. If it is still black try another charger, also try holding the charger at an angle. If this doe not fix it, remove the battery wait 10 seconds and try again. If this does not work you'll have to replace either the battery or the charging port and try again from there.
The issue seems to be the headphone jack. First take a flashlight and check the headphone jack. If you see any residue power off the device then lightly scrap a pin/needle against the inside. Turn it back on when you finish