After doing some search to ensure this wasn’t a result of the issue that started this crusade, I did some research focusing on the lost GUI and found the ‘Holy Grail’ - a TechNet Server and Tools blog post explaining the cause and solution. We apparently removed .NET 4.5 while trying to resolve our issue and ended up losing the GUI. The saviour post is: Removing .NET Framework 4.5/4.5.1 removes Windows 2012/2012R2 UI and other features
And this articles explains different ways to add and remove the GUI: How to Turn the GUI Off and On in Windows Server 2012
The sad part is, I can't remember the main issue that cause this entire situation.