Here is an Apple article on how to troubleshoot Magsafe charging issues:
If your MagSafe cable or power adapter isn't working - Apple Support
Assuming the Magsafe port is not dirty or damaged, then you most likely have some sort of hardware issue with this laptop. See if you can run the Apple Diagnostics to see if any hardware issues are detected.
Unfortunately there could be many things internally which could cause this problem and the only way to narrow it down is by testing with known good parts. First, I am always concerned about possible accidental liquid damage, but this is not always easy to spot. Even techs have a hard time recognizing liquid damage or noticing corrosion on the boards. Many times a magnifier and strong light are needed to see some very subtle signs.
Next guess would be a failing battery. If you have the non-Retina model, then the battery is relatively easy to replace, but unfortunately very hard to find a good third party replacement. The quality of third party Lithium batteries is extremely poor even when purchased from a respected vendor such as OWC or iFixIt. I recently had a defective battery from iFixIt which did not survive the calibration process....I'm waiting on a warranty replacement to see if the second one is any better. Next time I'm going to try a battery from OWC to see how it compares, although I have had OWC batteries go bad prematurely years ago (I've also had some very good ones...which shows how hard it is to get a good battery). These are the two best vendors as they are both respected vendors who have been around for years. OWC has official resellers located around the world.
You can try to see whether Apple will still replace the battery for you since Apple has mentioned they may be able to replace batteries for up to 10 years after a model is discontinued if the part is still available....this model was discontinued in 2016. An official Apple OEM Battery is the best option if possible. I will always choose an official OEM battery whenever possible.
It is also possible the DC-In Board is bad, although I have not had to replace them very often except when they are damaged. However, another user on this forum reported the DC-In Board fixed their charging issue (don't recall the specific details).
