It's most likely not the key. Even if you use an un-programmed key, the engine will turn over and start, but only run for a second or two.
It could be, but not likely, the starter. With no clicks or lights dimming or anything there is no indication the starter is even being told to make the attempt.
If your battery voltage is low or you have a bad ground or some such, the car might "decide" that there is not enough juice to make the attempt, but it sounds like you have a good battery.
This leaves us with the interlocks. If the car is not detecting that you are in Park, or Neutral, and the brake pedal is not pushed, it will not allow the car to start.
Have someone look at the brake lights when you push the pedal. Then try starting the car in Neutral or Park. If the brake lights are going on then we may suppose something in the shift linkage is not reporting position.
This may be due to a faulty wire somewhere...or a sensor or switch.