There's no power to the dashboard or to anything else thru the ignition switch until the switch is turned an extra 2 degrees or so. If I start the car and hold the key a bit turned (not enough to keep the starter motor running), the engine will run.
So now the problem is how ignition switches go bad, if there's a way to adjust this (I see a security star nut in the side of the assembly), and if there's any hazard in messing around with the ignition switch.