Faulty ignition/starting system

On my 1979 KE55 corolla, the car will start on ignition (next turn of key after ACC) not on start (last key turn position) and the starter motor continues to run once started. Is the starter/ignition circuit the problem or could the ignition barrel be faulty. (note: the ignition switch/barrel worked fine before i removed the engine)

You either have a bad ignition switch or the solenoid is sticking on the starter.