Try pushing the menu button. Does the menu appear on the screen?
If so you can disable any sleep function on the monitor in the monitors menu.
Occasionally a monitor will get locked on the wrong input after a computer has been turned off or cycled. Pushing the auto select button will often bring it around. Asus monitors have a good reputation. Unless you have male cats that like to mark monitors (I have seen it happen) the monitor is still probably good.