92 chevy cavalier - backup lights

I have a 92 chevy cavalier (automatic 4cyl) which has been recently having trouble starting I replaced the starter only to find out that it was probably the neutral safety switch. I followed the instructions exactly putting the neutral safety switch in however now the car starts in EVERY gear.
and the backup lights do not work. what could be causing this? I have tried 2 different neutral safety switches and it still starts incorrectly and the backup lights do not work