RealVNC installed on both would work. Its better than RDP* BUT ... Windows has to be healthy enough to allow installation of this software and able to connect to internet in order fro this to work. For RDP Windows has to be healthy enough and configured to allow RDP sessions over local network. If Windows XP, it would also have to be XP Pro and not XP Home. RealVNC will work with Home and pro, but XP Professional is the version you need for RDP sessions.
Additionally I would think you would want to get a new or used healthy keyboard for it to sell it, that is unless your selling the tower alone without keyboard/mouse and display etc.