Make sure you are fully in park, or drop the shifter to neutral (make sure you hold the brake pedal) and try to start in neutral.
The fact that you aren't even getting any sort of reaction when you turn the key says something else is up. There is another thing you could try if the first two suggestions fail but it is more dangerous. It involves jumping the starter relay, and it would take two people one to stand there and jump the relay, and one to hold the brake pedal.