Have you seen a message like this?
"This content requires HDCP for playback."
Movies purchased through iTunes are digitally protected by HDCP (High-bandwidth Digital Content Protection) to avoid unlawful reproduction, and require that the computer be digitally connected to an HDCP compliant device.
Rooms that do not have HDMI connections will not be able to display digital content protected by HDCP. For example you CANNOT use a VGA to HDMI adaptor, you must use the HDMI cable in the room to connect to your device.
For more information on HDCP, or for a current list of rooms that are HDCP compliant, please see the following solution: HDCP Playback in Classrooms.