Hi - you don't note/list the relevant settings/points:
In Settings > General > Monitors group do you have 'Select monitor for output display:' set to your external (usually second) display?
In Windows if you press the [Windows Logo][P] key combination with the projector connected are you using duplicate or extend for the display? It should be extend.
If you are using HDMI do you have the HDMI cable connected to the computer before you turn on the projector? Because of HDCP copy protection built into HDMI it can sometimes cause issues if HDMI cables are pulled out/connected while a signal is going through.