You have jiggled then connector while it is attached to the MBP, the contacts in the MBP and the charger are clean but the battery icon on the menu bar is black (not charging)? Have you inspected the thin wire that connects to the MBP, especially towards the housing and the connector? Twist them and see if there is an indication of a break.
If you have access to another charger, you could try that to see if yours is faulty.
This may not have a solution but look at it just in case:
OG's link got garbbled, should be Troubleshooting MagSafe and like OG says, if that doesn't work, another charger doesn't work, see an Apple genius bar for testing by the techs. A new charger is most likely to be the fix.