Seems I've encountered this issue several times over the last few weeks with Windows Server 2012.  I attempt to install updates and the progress bar will hang, essentially stalling out.  I cancel, I restart but I end up in the same place.

When I first saw this issue, I read something about setting updates to install automatically in the middle of the night which managed to get the updates installed but it doesn't actually solve the problem.

While attempting to install .NET Framework 3.5 from Add Roles and Features fails with the error:  "The source files could not be found".  Attempting to install from the .NET 3.5 Framework install fails pointing you back to Add Roles and Features.

While attempting to restore files from an NTBackup .bkf file, you might find a reference to the Windows NT Backup Restore Utility for Windows 2008 Server and not Windows 2008 Server R2.  If attempting to install the former, you'll be greeted with an error which basically states you need to add the feature "Removable Storage Manager" but you are unable to locate this feature.