Hello, A blue screen indicates a loss of video from the "Source". So whatever Input is giving you the blue screen is causing the issue. You mentioned "I also have an Apple TV but it always works fine". Please clarify what you mean by that? The Apple TV is also connected to the projector and doesn't give a blue screen? If so, then specifically what "Source" IS giving you a blue screen (DVD player, Cable Box, etc.)?
Please view my reply and send one back to proceed.