Overheating: Have you got any hardware monitor software to check for GPU temperature? If not, I suggest you download one in order to know what temperatures your GPU is working at.
The one thing which puzzles me is if the GPU was overheating or similar, it tends to crash the system in my experience (everything doesn't respond). You mentioned the lights and other things still working. Do they really still work? Or is it there are visible/audible signs they are switched on?
Driver: If there is an error mentioning the driver display, then it could have crashed or similar. Which version of the driver do you have? I've read that 16.7.3 has some issues which may be related:
http://www.gamersnexus.net/news-pc/2546-amd-mem-oc-limit-will-be-resolved-in-driver-hotfix This mainly refers to overclocked ones, but then some GPUs come factory overclocked. I'd check the details of your GPU to see if it corroborates with the info in the linked article. If your GPU is overclocked, then I think it may just be a case of either rolling back the driver and waiting for the hotfix.
Reinstalling may eliminate a corrupt driver.
http://www.guru3d.com/files-details/display-driver-uninstaller-download.html
Other thoughts: I noticed Speccy (at least it looks like Speccy) identified the iGPU in your system. Usually it would be automatically disabled in the BIOS when using a discrete GPU. Checking BIOS to see if it has been disabled may be something to look at (I'm not sure if there would be a conflict, but no harm in checking).
EDIT: much browsing and research has turned up multiple mentions of a problem with Windows 10 and nvidia drivers for multi monitor set ups. Have yet to see a mention of a solution at the time of writing.