1959 Chevy Bel Air ignition

Ignition switch on 57 Chevy is made to be held btiefly to engage the starter solenoid. Releaseing after enginge starts keep from burning out stater solenoid and starter motor. Is you Chevy box stock or has it been modified? Original ignition should have 4 positions, lock off, on, start. Since you have replace the ignition switch, did you replace with a 2 wire or 3 wire switch. If a 3 wire switch, ther should also be an accessory position, sounds like a 3 wire switch and you have crossed the wires, try swappin terminals on the hot side.

Did you put a hei/eletronic distribtor if so is the resistor/voltage drop hooked up? If its hooked up you will need to conect the two wires toghether the hei dist needs constant 12volts going through the resistor will drop the volts to 6v I had the same problem with my 55 chevy hope this works