MacBook Pro Retina 15'' Late 2013 Stoppped Charging
It is possible the logic board needs to be replaced. 

I would try resetting your SMC (manages the power in the laptop):


Shut down the computer.
Plug in the MagSafe power adapter to a power source, connecting it to the Mac if its not already connected.
On the built-in keyboard, press the (left side) Shift-Control-Option keys and the power button at the same time.
Release all the keys and the power button at the same time.
Press the power button to turn on the computer.


Note: The LED on the MagSafe power adapter may change states or temporarily turn off when you reset the SMC.

For the full Apple KB Article: https://support.apple.com/en-us/HT201295