Virtual Machine boots to unresponsive black window (but VM is actually running)

I installed Parallels 5.0 on a new mac mini and everything works fine except when I reboot the mac mini without a monitor attached. I have Parallels set to start the VM when the system boots although the same thing happens if I do not start Parallels on boot but connect via Screen Sharing and start it manually. The virtual machine starts, I see the BIOS and I see the initial Windows screen but then the screen goes black and never returns. I know the virtual machine is running because I can connect via RDP. If I shutdown the virtual machine (through RDP) and then connect a monitor I can quit and start Parallels backup up and it is fine.

I have the mini connected to a projector and I sometimes reboot the mini while the projector is turned off. This is the same as it not being connected to a monitor at all. It is not good for the projector lamp to turn it on just to reboot the mini and then turn it back off.

This may not be something that can actually be fixed but it would be nice.