There's a white, 1/4 or 3/8 " square about 2 - 21/2" long ceramic resistor on the firewall. It's the ignition system resistor. Smack it with a screwdriver handle & try again. That resistor is the bain of Dodge owners everywhere.
But if the engine will run with the key in the RUN position, that ballast resistor is NOT the problem. Don't touch it, or you'll break it.
The ballast resistor is used to reduce the voltage to the coil from 12 volts (nominal, actually about 13.4 volts) to about 9 volts for normal running. When the key is turned to the START position, there is a bypass circuit that's supposed to send a full 12 (13.4) volts to the coil, to facilitate starting when the battery is working hard to just crank the engine. The ballast resistor is NOT in the circuit during starting.
So the suggestion that the problem is in the starting bypass circuit makes sense, but I don't know where to start troubleshooting it.