How to recover contacts from an Android phone whose screen has died?
If the USB port were working on the phone it would probably be easiest to copy any or all of the phones data with a pc, however I surmise the screen defect was caused by the notorious shorted USB connector on Samsung phones. This being the case if you have another Samsung s4 5 or 6 one of the pieces of preinstalled softwares allows you to place 2 phones back to back to copy your contacts and settings perhaps that could help you.