I have a multi-monitor setup on a HDxxxx (don't know the exact model number). Some of the applications I use don't remember correctly the window position when I close them. So after placing them on the 2nd monitor and closing them, they will not reopen on the selected (2nd monitor).
For ATI/nVidia users there is these application (Hydravision/nView) that you can use to make these window position/location 'remembered'. Is there anything for intel cards?
I know that there are 3rd party application out there with such feature, but they are not free, and why would I use a 3rd party app when this feature should be built in with the graphics card's driver.
I am sorry you are having problems with the system but let me help you.
Note that the Intel® HD Graphics control panel allows the user to change settings but I regret to say that at this point is not possible to set under the Graphics & Media Control panel the window position.