C4in mesa

I've been trying to figure out what the problem is ? I replaced a connection on my starter yesterday. Car turned over 3 or 4 times. Today the car would not start. I took the starter off again to inspect the connections. I bolted it back on and got in the car. I put the shifter in neutral and it starts right up. What does this mean ? The neutral safety switch is still good if the car starts but in neutral not park. Tomorrow I need to get the shifter console apart and inspect the switch. Any tips please advise.