shut it down and then hold the power button and volume down (or up) for fifteen seconds. it should vibrate three times. then you can use the volume keys to navigate to the restore to factory settings option
When it boots up hold command & R to boot into recovery mode. Open Disk Utility and reformat the drive you are using. Then quit Disk Utility and open Reinstall MacOS Sierra and follow the onscreen instructions. Also you can hold shift, control and option to reset the SMC.
Most probably your MagSafe board is dead. to remove it you must remove the logic board then unplug it from the logic board. They are very cheap, usually about 10 bucks on eBay. Hope that helped, looks like you spent a lot of money on logic boards.
What could have happened was the keyboard cable got disconnected or cut. A similar thing happened to my MacBook Pro. What you can do is unscrew the bottom plate, and when the computer is plugged in, create a short between these two pads. This will basically be the same as pushing the power button. If you want to repair the keyboard and trackpad, unplug the battery and power adapter. The battery connecter is located on the far left beneath the power pads. Check the other cables next to the battery connector for breaks or if they're disconnected. and if they are fine that must mean that the cable has been broken further along the line. To find the break you have to remove the logic board. Just Google 'how to remove logic board on macbook air 13'. Hope that fixed your problem.