Why will my projector not turn on?

Thats good you checked to make sure you had the power cable plugged in and it was a good outlet because that is the initial troubleshooting step. Next try to clean out all the vents and filters because an accumulation of dust can cause the projector to not turn on. Following this logic verify that the cooling fan is functional and cooling the unit properly, the build up of dust and poor ventilation can cause the unit to overheat and if the fan is not properly cooling the unit and it overheats it will not turn on. Lastly if the unit is plugged into a good outlet and well ventilated and continues to not turn on you will need to replace the main board.