All the neutral safety switch does is provide a ground to the starter solenoid so there's absolutely no way it could cause the starter to engage. Do this as a test. Next time you start it up pop the hood and the top off the relay block that's right behind the battery and remove the starter relay. Then go put it in gear and see what happens. By removing the starter relay you effectively unhook the starting circuit. If it still makes the noise it's nothing to do with the starting circuit and must be a mechanical problem
