MacBook Air 2012 won't charge or boot
A similar thing happened to my MacBook Pro - from around the same era.

The only other thing I would suggest is trying a few different wall power outlets and making sure those outlets are working (like with a lamp).

Other than that the unfortunate diagnosis is that your MacBook will most likely have a dead logic board.  On the Airs, I am pretty sure most things are directly integrated to the logic board:, RAM, CPU.  But the SSD is removable and you could take it out and put in into another Mac to get your data from it, if need be.

Here is a guide on how to take apart that model of Mac Air.