Lets first check the MagSafe cable and the connector for any damage, Is the cable smooth and not have any bunching up or cuts? If it does you’ll likely need a new charger.
Next look at the connectors both the cable end and the systems. Are the contacts clean and shiny is the socket plastic clean of dirt buildup? Use a cotton Swab (Q-Tip) dampened with isopropyl alcohol to scrub the surfaces and use a fresh pink pencil eraser (soft) to clean the contacts. Are the pins in the cable aligned correctly the middle pin will be not as high. If either fails to get clean or the pins are not aligned then again time for a new charger.
The chargers MagSafe connector LED needs to offer either an Amber or Green light when plugged in. If it doesn’t I would try another charger make sure you get the correct one for your system. And stick wit a Real Apple unit as the knockoffs can kill your system or worse!
* [https://lifehacker.com/dont-replace-your-macbook-charger-with-a-cheap-knockoff-1825605569|Don't Replace Your MacBook Charger With a Cheap Knockoff]
* [https://beetstech.com/blog/oem-magsafe-chargers-vs-counterfeits-teardown-for-truth|OEM MagSafe Chargers vs Cheap Imposters: Teardown for Truth]
* [http://www.righto.com/2016/09/why-you-shouldnt-use-cheap-macbook.html|Lacking safety features, cheap MacBook chargers create big sparks]
* [https://www.youtube.com/watch?v=DrxAuhrrLU4|FAKE Magsafe MacBook Chargers on eBay - Watch before buying a Mac Charger]
Here’s the correct charger for your system: [https://www.apple.com/shop/product/MC461LL/A/apple-60w-magsafe-power-adapter-for-macbook-and-13-inch-macbook-pro?|Apple 60W MagSafe Power Adapter (for MacBook and 13-inch MacBook Pro)]