No Crank, No start

I have a 98 Corolla 240K miles. It started intermittently for a month or so. If I turned the key I got nothing, I would rock it, or try to push start it (manual transmission) and it would start just fine. I thought the solenoid was bad. I replaced the starter, same symptoms, then the starter relay, the fuses and the ignition switch. I even replaced the neutral switch. Now when I turn the key to start, it cuts all power, no dash lights, no crank. I rechecked the relay and starter switch, all good. Any ideas?