Hi Guys,
I had a very similar problem that you are describing gman. In my problem, it was the ignition switch. Exactly what eagle stated, the switch had melted on a couple of the runs in it. It was so bad that it melted the plastic on the outside of the runs. At first, the Jeep would start and then when I let go of the key it would shut off. Then the problem got worse and I could not start it at all. Swapped the unit out, BTW PITA. Jeep did not want "you" to replace that part they put pins in the star bolts so you could not get the tool in it. Just break them off with a small flathead screwdriver. Also, if you have an airbag, PLEASE make sure that you know how to disable it and remove it before attempting to replace the bad part.
Alex
Do you want a schematic or a parts breakdown?