The best way to resolve this problem is take your laptop off any external display, then change the refresh rate for your built-in monitor from 60Hertz to 40Hertz. If you plug another monitor into the computer it will quickly recover, but after it has been removed the problem reoccurs. The only reason it works on a docking station is because of the external video. This is a well known problem with this particular HP product. In other forums, people will say that the way to solve this problem is to put it on a docking station which is incorrect.
HP EliteBook 8440p screen will go to sleep while you are working on the laptop and won’t wake back up, even if you try to press keys or move the mouse.