I have an 11" MacBook Air purchaed new from Apple Online in November 2012.
Today the MBA won't turn on. I left it sitting on my desk overnight plugged in to the original charger to have a full battery in the morning. This morning it would not turn on at all. Tried holding down the power key for an extended time, no result. The green light on the charger glows when it's plugged into the MBA.
I went to the Apple support page and followed the instructions, i.e., "PRAM" & "SMC" (Command-Option-P-R, until you hear the startup chime --and-- "Press (left) Shift-Control-Option along with the power button once)
... but still no result at all.
I have taken extreme care to not add any 3rd party Apps or software. I use this laptop almost entirely with Office software only and Apple Mail / Safari browser specifically so that I never have issues with conflicting software. When I put this MBA into service I didn't even do a Restore from my previoius MBA with the idea of keeping it as innoculated as possible from any 'legacy' issues (whether real or imagined).