I have a bizarre problem with my 2012 MacBook Air 13":
At some point, a couple of weeks ago, it suddenly stopped turning on. The battery would charge, but pressing the power-button just wouldn't have an effect. I clearing the SMC by pressing Shift-Control-Option, which didn't have any effect. I tried different power adapters.
Then in a last-ditch effort I decided to open it up. Much to my surprise it did boot up just fine after: disconnecting the battery, pressing the power button (with AC not attached), reconnecting the battery, reconnecting AC power, and pressing power.
The weird thing is that everything (including the power button, going to sleep etc) just works, just when I shut down OS X completely, the same problem occurs (all the times), making it necessary to unscrew the bottom and do aforementioned procedure again ;)
Have anyone heard of this problem before? Are there some specific components on the logic board that could be causing this? (I am not sure if it's worth having this repaired through official channels.)
Update: To clarify the symptoms when the Air doesn't boot up: black screen, no fan, no keyboard backlight (or anything else that would indicate that it is running).