MBA mid 2011 2.9 Firmware update just killed by Air

I had the same issue. The machine simply shuts off and doesn't restart so the firmware update is never applied. The power button stopped working and the machine would not turn on at all. So I took it the the Apple Store and they cracked it open to do a physical SMC reset. It booted up fine after that. We tried the install again and no dice. Same thing happened. This time the guy at the Genius Bar did some kind of "soft" SMC reset. He pressed SHIFT+FN+CONTROL+POWER at the same time (the first 3 keys are in the lower left corner) ... held it for a few seconds and let them go. When he pressed the Power button after that the machine booted up fine. Still didn't apply the firmware update though. The guy at the Genius Bar said he would report this issue to Engineering to alert them to the problem with the update.

In any event, your laptop is probably not completely dead. Give that keystroke combination above a try to see if you can revive it. It doesn't appear to be the standard SMC Reset keystroke combination which is SHIFT+CONTROL+OPTION+POWER if I recall correctly. Certainly wasn't anything I'd ever seen before.