If you've got a points type ignition, this is the classic symptom of a bad ballast resistor. The car uses 12 volts to start, but when the switch goes to the run position, it uses another wire to feed the distributor's points. That wire has a resistor somewhere inline to reduce the voltage to the points from 12 volts to around 6 volts. When the resistor fails, the circuit goes open, and no juice gets to the points--immediate shutdown! Find a wiring diagram and start looking for that resistor. Good luck.