Chosen Solution
From what you have show us in your snapshots it appears the charger is not being seen at all! We need to walk the pathway from the MAgSage charger plug into the system and then the pathway internally. Review this Apple T/N Apple Portables: Troubleshooting MagSafe adapters make sure the cord and the MagSafe connector are in good shape if not you’ll need a new unit. While the charger worked on another system its possible the connection is loose so it sometimes works. Next we need to make sure the MagSafe connection on the system is good. You may need a new unit look at the guide for the needed part MacBook Pro 17" Unibody MagSafe DC-In Board Replacement I’ve often see the plastic plate warped so the pins don’t make contact to the MagSafe charger pins as well as blackened contacts which just won’t pass the power. If you have a DVM you can check the voltage at the logic board. Let us know what you discover!
