I understand your problem and let me help you to solve it.
It is important to mention that if a video card is connected to the PCIe on the motherboard, the onboard graphics will be automatically disabled. So in the case you want to have 3 monitors configuration, the video card must support the three monitor setup.
If you try to use the onboard graphics, you must have the following configuration:
Display Port + HDMI+ DVI
Display Port + DVI + VGA
Display Port + Embedded display +HDMI
So basically you must have at least 1 Display port connection and have a direct connection to the monitors (no video adapters).
You can try the latest driver for your controller here:
That's not correct. I can use 3 monitors, 2 linked on my nVidia 770 and the 3rd on my integrated intel output at the same time. It always worked like this and I never seen a system that won't allow it unless the iGFX was disabled on purpose in bios.
That said, I fixed the problem with the devcon fix Workaround for black screen problem . This is a bug in your drivers, hundreds of people are reporting it on this forum and on other well known hardware forums worldwide. Your driver make all the HDMI/DVI ports (on different GPU cards) stop working after the intel one has been initialized at boot. The fix is to run a task at boot which disable and re-enable the intel integrated card via the devcon Microsoft utility.
PS: You even have a sticked topic for this problem in this forum. Fix your drivers.