70 chevelle 396 won't start

I have an audio shop and we were working on this chevelle. From the begining, something didn't seem right with the key cylinder when starting the car. When the key is turned, the dash light and radio come on, but the car doesn't attempt to start. The battery is fully charged. My guess is it is something with the starter or neutral safety, but I really don't know. I tried starting the car car in neutral and jiggling the shifter (automatic shift) but that didn't work. If anybody has any ideas, it would be greatly appreciated. Thanks.