I'm having the same issue with the same GPU
. When I connect my HDTV by HDMI the GPU recognizes the HDTV, switches to it, and Windows no longer recognizes the monitor connected by DVI.
The DVI monitor works alone but not with the HDMI connected.
I checked for the monitor in display settings and nVidia Control Panel but it can't be found there either.
Thoughts? I've updated and rolled back drivers to 270.51.