System boots on the secondary monitor with dual screens
(Windows 10, NVIDIA nvidia quadro p2000)
Had a similar problem with a triple monitor setup. The solution was to boot into the BIOS and switching plugs going into the graphics card (while still in BIOS) until the correct physical display showed up.
Windows seems to identify each display by some hardware ID because it still shows them in the same physical order, including primary screen that previously was set in settings, once back in Windows, the display numbering in Settings/Display changes though and apparently is related to the ports.
I know that this is an old thread but I had the same issue with a nVidia Quadro P400 where the monitor plugged into the No 1 slot in the card would work fine so long as nothing was plugged into the second slot (a second monitor). As soon as I plugged in the second monitor into the No 2 slot the first screen would go blank and the second screen would become the primary screen and I couldn't override it. Extending the screen would make the first screen identify as 2 and the second screen would identify as 1.
This would cause intermittent issues with booting up where the system would hang and the mouse cursor would display on the right-hand monitor.
The solution for me was to plug the second monitor into the No 3 slot instead of the No 2 slot and then everything worked as expected and the left hand monitor would identify as 1 and the right-hand monitor would identify as 2.
Nothing else worked. I recognize that this will not be a solution for cards with only two inputs but might help those of you with cards that have three inputs.