My MacBook air won't start? Black screen

I closed my MacBook air and when I opened it again it won't start. I tried to reboot it but the screen stays black. I hear the ventilators turn slowly when I try to turn it on but nothing else happens. The light on the macsafe charger is on. A few hours earlier the charger won't work but the MacBook worked well. After a while it worked again and I charged the computer and surfed on it without the charger later. It happened a little later. I tried to reset the PRAM and the SMC but the screen still stays black. I tried to start it with a external hard drive but nothing. I tried to connect an other screen but still nothing. I'm desperate!

I have an appointment at the genius bar next Tuesday but I hope it will start again until then.

What can it be. Is it possible that the charger had a diffect and that something overheat?

Thanks in advance for your help. And sorry for my English, I'm french.