Replaced switch but will not start

Went to start car one day and key turns lights lights on dash come on but no crank. Checked battery, is good. Unplugged ignition switch and can jump start. So thought ignition switch was bad. Replaced switch, still does same thing. Put new key switch in but wont go all the way in. Used old switch goes in fine. Noticed a small white plastic piece between elec, ignition switch and key assy looks like might be broken it turns very easily, does it have anything to do with not cranking?