Thanks Everyone. I contacted Dell and they told me this monitor fully supports HDCP including 1080p:
Thank you for contacting Dell Warranty Support. I understand that you are getting an error when trying to play DVD using 1080p HDCP on your 2407WFPb monitor. I apologize for the inconvenience that you have been experiencing. I appreciate your patience with this matter and I am glad that you e-mailed us to help you.
Yes, this monitor supports HDCP.
Video Supported Modes
Video display capabilities (DVI playback) 480p/576p/720p/1080p (Supports HDCP) Video display capabilities (Composite playback) NTSC/PAL Video display capabilities (S-Video playback) NTSC/PAL Video display capabilities (Component playback) 480i/480p/576i/576p/720p/1080i
You may refer to the following:
Moving forward, this article may be helpful to your concern: