I'd check ifixit.com to see about replacing the "DC in board":
(note -- this says "early 2013" -- just to be aware):
If your MagSafe 2 power adapter has been damaged, you can replace it. Use this guide to install a replacement MagSafe DC-In Board.
www.ifixit.com
If you do order a DC magsafe from iFixit, you may end up worse off. I just did a top case and battery swap on my early 2013 MBP. While in I figured I'd update the wi-fi board to 802.11AC and replace the magsafe board as preventative it was looking pretty chewed up. I ordered NEW, paid for NEW... held off on my repair for 2 weeks for it to arrive, it was in a sealed static bag and was obviously used. I contacted them, they said they don't have any new in stock so shipped what they had (keep in mind they never asked if this was acceptable or reduce the amount I paid to the price for used. I said no, I wanted new, I will wait for them to come in. A MONTH LATER, it's shipped, arrives sealed in anti static and it's... you guessed it.. USED!!!!! Not even a simple we're sorry etc... ship them both back to us and we'll give you your money back. A month and a half dicking around and ended up ordering one on Amazon for $12.00, about $20.00 less than I was paying iFixit, they'll never see a penny of my money again, that was very unethical.
Jen