Basically I was watching a movie the day before without plug in the Mac-air 11.6, I felt asleep and the day after I couldn't used it anymore, no signal, It's dead. Never drop it.
Portables that will not Power on.
Try another power outlet.
Go step by step.
Note: Steps 5 and 6
Reset SMC. http://support.apple.com/kb/HT3964
Choose the method for:
"Resetting SMC on portables with a battery you should not remove on your own".
Retrieving data ...