Why does my car intermittently fail to crank?

Actually, almost no one can get the car to start but the wife. It fails to crank for her half the time. I have changed the battery, ignition switch, ignition key cylinder. No blown fuses, links or relays. No engine codes. There is power to everything else. Can hear the fuel pump running and the pressure is ok. There is no sound at all (clicking, etc.) When it does start, it fires immediately and appears to run very good. We have watched her when successful and cannot see her do anything different from us. When this problem is occurring, it makes no difference what gear (automatic), brakes or not, steering wheel position, or the "jiggling" of any of these.