The recent warm weather had made using my 3 monitor configuration a little uncomfortable. To make things a little more bearable I decided to turn off two of the monitors to reduce the amount of heat output into the room. I disabled the monitors using the display settings in Gnome 3.28. All was working well.
Today I attempted to re-enable the screens and here a problem arose. Whilst my DVI connected monitor powered up correctly and could be managed in display settings, the HDMI connected monitor could not. The HDMI cable was exchanged and the monitor confirmed to be working by connecting to a laptop. I had begun to suspect a faulty HDMI port on the graphics card. No amount of powering down and rebooting would solve the issue. However the monitor would display the BIOS screens and boot process up to and including the login manager. The only point at which it would fail to display anything was upon logging into Gnome.
Some research pointed to a monitors.xml file. This can be found in the users home directory ~/.config/monitors.xml. Opening this in a text editor and reviewing the contents showed that it had become corrupted. It showed monitors connected multiple times to different inputs. In the past some of this information would have been correct, but as my monitor connections have changed the file had not been kept up to date.
I removed the file, since it gets automatically regenerated, then logged out of my session. On logging back in my HDMI monitor became enabled again and working alongside the others. I was then able to tweak the display settings to have them all back to my desired configuration.