If the MageSafe LED is not lighting you need to try cleaning the MageSafe connector as it often collects dirt. Give it a good clean both the grey sides and the black bottom plastic areas, for the contacts get a fresh pink pencil eraser to scrub the contacts.
Did that work? If not you may need to replace the [parts|MacBook Pro 13" Retina Display Mid 2014|DC In-Board unit|itemtype=magsafe_boards] following this guide [guide|27846] did that fix things?
Lastly, if neither of these fixed the problem your logic board has an issue which will need deeper diagnostics.