I have Intel DZ68BC motherboard with IntelHD graphics card using two monitors (on DVI and on HDMI->VGA). My friend asked me to test if his NVIDIA graphics card works well on my computer (at his it was doing some trouble), so I inserted it in my computer, installed NVIDIA driver
and it worked quite well. Then I removed it, uninstalled everything nvidia-related i could find and switched monitors back to my Intel card. Since then after every system start/restart system sees only monitor on HDMI->VGA connector, completely ignoring DVI monitor.
I noticed that installing Intel video drivers
causes system to recognize second monitor if I don't immediately reboot. After reboot system recognizes only HDMI->VGA monitor.
I also tried starting in safe-mode and using DriveSweeper to remove remains of NVidia drivers. While it seems that some drivers were removed, situation didn't change. Now I am out of ideas and I really wouldn't like to reinstall system (again...).
I also tried Restoring system to state before this whole story, but it also didn't change anything.