First...Check that all cables are connected correctly..If they are then look at the condition of the cables you're using to see that they are not damaged..Second..Your projector has a lamp that may need to be replaced because even though your unit may not show you a picture then seeing the light will eliminate having to replace the bulb
What is the exact model number of the Sony TV? Check if the same issue occurs when connected to a different source device like DVD player or when the TV is not connected to the cable box. Disconnect the connected devices and turn ON the TV to check if the red light still flashes
