Have you checked the battery? Measure its voltage. If low, charge it with an external charger. When charged completely (measure again to confirm), let it sit for a couple of hours. Measure voltage again. If still charged, try starting. If it starts and then dies, i guess it could be an alternator- issue(?)
Check that there is no pocket-lint or other debris in the port. Something might be shorting the pins of the port. You can also try cleaning the port with a toothbrush with some rubbing alcohol on it. And/or blow on it with some compressed/canned air. Also, Look into the port with a magnifyer or use phone camera and zoom in, to see if any of the small pins look out of place.
I'd say, start by taking the controller apart and give it a good cleaning. There are good disassembling guides on youtube. Remove the bumpers and scrub the plastic parts with water and washing-up liquid. You can also use a cotton swab with rubbing alcohol to clean the inner frame and around the button (where you do not want to use water). Use an online gamepad tester to test afterwards. Then you'll easily see if the problem is gone.
