You should be able to sign into RealPlayer with your email address as it is associated with your RealPlayer Plus. You can officially sign into 3 different computers concurrently. Can you please let us know what happens when you try to sign in on the desktop? Are you seeing any error messages?
In the meanwhile, to resolve your issue, please "over-install" RealPlayer. Over-install simply means installing RealPlayer over the existing RealPlayer. When you go through the installation process, you will be prompted that RealPlayer is already installed, simply proceed with the installation when prompted.