Keyboard / Trackpad not working in Mac OS, but works on boot screen and in Windows
So my final answer is that this is probably a firmware problem and you need to re-flash it, unfortunately Apple doesn't allows users to do this on Macbook Airs. You'll need to take it to your local Apple Store for the genius to do it. If it is indeed an hardware problem, Apple Stores have access to a more detailed system diagnosis, which will almost certainly tell you what the problem is if it isn't firmware. 

Sorry for the long time and hope you can solve it.

Tiferrei