Greetings Azadeh_1,
What model ASUS laptop do you have?
If possible remove the battery and unplug the power adapter. Then hold down the power button for 30 seconds and try again.
Plug your device to an external monitor to see if the display is defective.
Not sure about the two power buttons part, could be another function like sleep or a special feature specific to your laptop.
Let us know so we can better help you out.