With Web Application Projects, you shouldn't be adding App_Code folder. It is intended for Website Projects. With Web Application projects, all your class files are anyways compiled.
The same result can be achieved by creating any folder (MyCodeFiles) and having all the class files inside it. That is why there is no option to create an App_Code option in the VS menu.
If it works, can you try adding a custom folder and see if it has any issues? If you still need the App_Code to be there, then try checking the namespaces of the files & the build action again.