Ctrl Alt F8 disconnects displays?
Just stumbled across this now. In the hope it helps someone else, and in addition to the accepted answer, here is how to re-connect your 'disconnected' display(s) in Windows 10:
Right Click on the desktop and select display settings:
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Click on the icon for your disconnected display:
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Scroll down, down, down and select Extend / Duplicate form list:
What causes this is additional software that comes with the Intel Graphics chip. This software monitors for the Ctrl + Alt + F8 shortcut and then resets the display settings to a default value.
While the "Intel HD Graphics Control Panel" setup utility allows configuring keyboard shortcuts for other tasks, it does specifically say that you cannot change or disable the shortcut for the "reset settings" task.
The only way to disable this is by disabling the Windows Service installed by the Intel Software.
Go to Windows Services list
Find the "Intel(R) HD Graphics Control Panel" service.
Disable it (open its properties, stop it AND make sure to set its startup type to "Disabled")
You may need to reboot the computer once.
Note that this answer was written in 2016. Newer versions of the Intel Graphics software have options to disable the hotkey without having to disable the service. See the comments of this answer on superuser