If the installation ran OK (though obviously managed to miss something along the way) I would first try the same installer again. As you have it there already it will only take 5 mins and can’t make things any worse!
I don’t believe you need to download the installer again. Just uninstall Cubase Pro 8via the Windows Control Panel (only the Cubase application, you don’t need to uninstall anything else. Leave all plugins and content files as they are) and run the Start Center again. Only Cubase pro 8 will be re-installed.
I can’t tell why your skin file got corrupt, but re-installing Cubase will help.