Sounds like it's electrical since it dies instantly like you turned off the key. If it was fuel, it should start running rough and die slower I would think.

When the car is running, the ignition gets power from the blue wire coming from the ignition switch. When it dies(before you touch anything) make sure you still have power on the blue wire. Test for power at the base of the steering column at that connector. Also check for power on that wire at the bulkhead connector and work your way into the engine compartment.

I'm not sure if a failing ballast resistor will cause the issue or not. It could be getting hot and not passing any current. Usually they just fail completely though. It could also be a problem with the coil. I'd start by confirming power on the blue "run" wire when it dies though.

EDIT: I just re-read your post and it sounds like it only died once. I thought it died multiple times. Since it only happened the one time, I'd start by cleaning all the contacts on the steering column connector and the bulkhead connector. If there is some condensation in the connectors it will cause them to get hot and possibly melt. When you take those connectors apart, make sure there are no signs of heat. Once they are clean, use some dielectric grease on them to keep out the moisture.