Sometimes the car will not turn on

I have the car on Neutral or Parking. Then I turn the key to start the car and all the lights turn on, but the car does not start. There are no sounds. As if the battery was dead, but the battery is fine because the lights turn on and after turning the key on and off a few times, it starts. If it has started and I turn the car off and try again, I have the same problem. Its like a fifty percent chance that the car is going to turn on. I think there is something wrong with the starter.