Maybe just a bad ballast - maybe something a bit more complicated
There are 2 sources of 12 volts at the ignition ballast.
The first (dark blue wire) goes through the ballast and sends reduced voltage to the coil during normal driving when the key is in the "run" position. (a.k.a ign 1)
The second source of 12 volts (brown wire) is on the other side of the ballast (2 wire side -one wire goes to coil and the brown comes from the "start" position of the key switch) and provides a full 12 volts to the coil during start up. (a.k.a. ign 2)
It sounds as though you have 12 volts in the "start" but not the "run" position of the key switch. That is why it runs in start and then dies when the key switch is returned to run.
Check for 12 volts on the single wire side at the ballast with the key in the run position.
If you have that you should also have a reduced voltage coming out of the other side of the ballast.
When this happend to me the problem was in the connector at the key switch.
The "hill-billy" test is to run a 12 volt jumper to the ballast on the single wire side while leaving the stock wire disconnected and try to start the engine.
If it runs then you have to figure out why there is no 12 volts from the key switch in the run position.
Many times someone at some point in the car's life will have tapped into this wire for a keyed 12 volts to power their "bitchin" new tape deck. Look carefully for any suspicious looking electrical tape, or wire nut splices under the dash. A bad connection will cause this as well.
If you dont have this in your library; download and study this.
http://www.mymopar.com/downloads/1969/69BelvedereGTXSatelliteRoadRunnerFull.pdf
Hope this helps.
