I have an 01 Deville DTS and am experiencing some very strange issues. I know my way around this car well but really need some help on this one. Here's the issue:

Ran fine at Noon. 5:00pm turn the key and nothing. Dash lights come on, if I jiggle steering wheel some of the dash lights start to flicker. If I jiggle steering wheel while holding key in start position you can hear starter solenoid click and it even turned over a bit and fired but immediately died. Turned key and took out but could still hear a hum, possibly fuel pump? Jiggled steering wheel with ignition in off and key out and realized the wheel didn't lock. it locked but still heard humming, jiggled with wheel locked and it shut off and doors unlocked. put key in and tried to start again and nothing, tried to turn key back to off and could only get key to turn back to first click. Called tow truck. on the way home you could see head lights flickering as we hit bumps.
Got it home and pulled off steering column covers. I can see no bare or disconnected wires, no wires that had insulation cut that I could see. started trying to start again while jiggling steering wheel and the car started. I let run for 2 or 3 minutes and ran great. turned wheel several times and shut car off. fired right back up repeatedly. 1 hour later the car was back to not starting.


The ignition switch on it is less than a year old, replaced by a Cadillac dealership.
I replaced starter approx 2 years ago.
Battery is 6 months old and tests good.

I towed to shop for diagnostics but they have had all day and at 5:00pm they still hadn't figured it out.

Anybody help me out with this?