Removing the power to a device often enables it to restart. Obviously just disconnecting the magsafe from the MBA doesn't achieve this as the battery is still connected. Having attempted the SMC reset with my dead MBA I tried disconnecting the battery. This solved the problem, after reconnecting it the MBA restarted and I then did the SMC reset and NVRAM reset for good measure.
So - how to disconnect the battery? If you remove the backplate there is a connector for the battery which you can simply pull off the logic board. The location of the connector varies with the model and year so google 'remove battery from macbook air' for your model. You don't need to actually remove the battery, just do step one which is remove the connector.
But - how do you remove those tiny screws that hold the backplate on? Here's the catch. You need a 'pentalobe' screwdriver which you'll probably need to send off for if you don't have one. (I did, from having upgraded the SSD). What a drag but a lot cheaper than an Apple service bill if it works.
"...I tried disconnecting the battery..."
I just had a remote user (on the other side of the country) with a 2011 MacBook Air that would not turn on. At startup the machine chimed, the screen flashed, then nothing.
The user took the MacBook Air to an Apple Store as a last resort (before overnighting it back to me for replacement). The guy at the Apple Store simply opened the back, then disconnected & reconnected the battery.
It is now working again.
I wonder for how long?