My macbook air (2016) won't turn on

Try resetting the SMC How to reset the SMC of your Mac - Apple Support

Notebook computers with a nonremovable battery

This applies to all MacBook Air models, as well as MacBook and MacBook Pro models introduced in mid 2009 or later, excluding the MacBook (13-inch, Mid 2009).

1. Shut down your Mac.
2. On your built-in keyboard, press and hold all of these keys:

• • Shift  on the left side of your keyboard
  • Control  on the left side of your keyboard
  • Option (Alt)  on the left side of your keyboard

1. While holding all three keys, press and hold the power button as well.
2. 
3. 
   
4. Keep holding all four keys for 10 seconds.
5. Release all keys, then press the power button to turn on your Mac.

Hi,

You'd better contact Apple Support to tell them the circumstance you face with now or take your MacBook Air to nearby opened Apple Authorized Service Provider to be examined it.

https://support.apple.com/contact

https://locate.apple.com

I tried this multiple times. Took it to Geek Squad and they did not resolve.

I wouldn't expect geek squad to figure it out. As suggested above by kaz-k you should probably take it to an Apple Store genius bar or an AASP for service.