Ballast resistor, the engine runs when the starter solenoid is pulled in and then dies once the starter stops.
With the ignition switched on, check you have power into and out of the ballast and to the coil.
In doing so you will confirm the integrity (or lack of it) of the ignition switch and wiring run to the ballast resistor, the integrity of the resistor itself and finally the the wiring from the ballast to the coil.
