With the monitor disconnected Windows is running headless and doesn't render the desktop. A common way to work around this when GUI testing is to create a console session with your machine and leave it open.
You can use something like VNC server running on the testing machine and leave a connection open to your testing machine. My preferred method is to run tests on virtual machines and use the vm software to keep a session open with the machine. You could also make RDP connections from a PC to your testing machines and leave the window minimized as per these instructions:
http://support.smartbear.com/viewarticle/56551/. IMO leaving a session open using VNC or virtual machine tools works way better for long term testing on remote machines.
This article explains it well:
http://autumnator.wordpress.com/2011/11/18/how-to-run-remote-headless-gui-automation/
