Have you tried an SMC Reset?
Have you inspected the Magsafe port on the laptop to see if the contacts are clean and to see whether some metallic object may be stuck in the port due to the magnet which may prevent the charger from seating fully? I find a lot of staples stuck in the Magsafe port...sometimes they can be very hard to see since they can get pushed into the corners of the port.
Try unplugging the power adapter from the electrical outlet for a minute to reset the charger's internal circuitry. And try using another electrical outlet.
Does the Magsafe LED light up, is it solid or blinking? Amber or green? Or red?
Here is an Apple article with Magsafe charging troubleshooting tips:
If your MagSafe cable or power adapter isn't working - Apple Support
Try running the Apple Diagnostics to see if any hardware issues are detected.
Like @Rudegar mentioned, just about any MagSafe 2 charger will work even if it is a larger size since the MBAir I believe only requires a 45W charger IIRC.
Have you checked the battery condition in macOS? A bad battery may prevent the laptop from charging as well.