Thanks for the info Tmontefusco but I think you are still misunderstanding my question.
Yes, I am using self signed certificates, however I'm not concerned with the process of getting it all setup. My question was in regards to the fact that ArcGIS Server got put into a state where I was unable to access any of the management tools (which all of your links require). I was hoping for instructions on how to recover from the problem, NOT turn on security. The information I provided concerning security was simply to provide background into what caused the problem.
I managed to fix my own problem by reinstalling ArcGIS Server. However, even after re-installing ArcGIS server the first time, the problem persisted until I removed the arcgisserver directory (containing config-store, directories, logs) and then re-installed again.
My assumption is that I probably could have removed the arcgisserver directory and triggered a re-initialization somehow, but deleting the directory and re-installing does work.