Which mode are you using? From your description it first looks like Extended Desktop, then again in the headscratch sentence I get the expression of Clone Mode. What happens if you choose the projector only as your display? Clone Mode should also work.
Also, and I don't know if there's any difference, what method do you use to choose between different multi-monitor modes? Video card Control Panel, laptop Fn + F-key combination or Windows-button + P, or maybe some other? IMO Win+P is the easiest way to change between modes.