A SafeBoot Start up your Mac in safe mode - Apple Support will sort many anomalies
Reboot as normal and test.
ref:
If your MagSafe cable or power adapter isn't working
Unplug the power adaptor from the wall, wait 60 seconds and then plug the adaptor back in.
If your MagSafe cable or power adapter isn't working - Apple Support
If your Mac battery status is “Not Charging” - Apple Support
If your Mac battery status is “Not Charging” - Apple Support
The rule of thumb—if you are near the mains leave it plugged in, if you need the portability then run on the battery only—this is how you help optimize your battery charging and extend the working life of your battery by reducing the cycle count.
Get help with your Mac notebook battery
Learn how to optimize the life of the battery in your Mac notebook, fix battery issues, and get service.
If you see Service Recommended on your MacBook Air or MacBook Pro - Apple Support