Your problem is that you are changing the root directory to the wrong thing!
Based on your screenshot, your content project is called "GameStateContent", and using the default template will be created in a directory called "GameStateContent". That is the directory to which Visual Studio will copy all the content files you drag onto that content project (if they are not there already).
But the output directory (the thing in brackets, in Solution Explorer) is still "Content". This is where the content project outputs the XNB files that it builds from your input files. So if you tell XNA that the content root directory is "GameStateContent" then it will be looking in the wrong place!
If you click the project and press F4 to bring up the properties window, you can change the root directory.
ContentManager in XNA basically looks for XNB files in the directory you specify, next to the game executable. You can go in and look at that directory in your project output directory. It will probably be:
Go in and have a look for it, check it has the right name and contains the right XNB files.
I don't understand why your game project has a "Content" directory (or bin and obj, for that matter). Or why there's another "Content" directory in your GameStateContent project. You can probably safely remove those.
Providing you haven't made any other strange changes, you should be able to simply set:
Content.RootDirectory = "Content";
and have it work.