Try an SMC reset and a PRAM reset (hold the PRAM reset for at least three chimes).
Run the Apple Diagnostics.
Here is an Apple article for troubleshooting Magsafe charging issues:
https://support.apple.com/en-us/HT203207
Make sure to unplug the charger from the electrical outlet for a minute to reset the charger's internal circuitry. Also on some computers I need to wiggle the magsafe connector or make multiple attempts to get the magsafe LED to light up. If you have the "L" shaped magsafe charger make sure the case isn't damaged or deformed which can prevent the "L" style magsafe connector from sitting securely. Any defect in the case around the charging port will prevent an "L" style charger from working.