If it starts but dies as soon as you let go of the key, that's a classic sign of a bad ballast resistor. The resistor gets bypassed in the START position. That's why it starts just fine but dies as soon as the ignition switch moves to the RUN position.

It could also be a problem with the bulkhead connector, steering column connector or ignition switch. Use a test light to confirm you have power where you should...when you should. Test the blue wire that's connected to the ballast. You should have power there with the key in the RUN position.