do you have to hold the key to run the car, or it will cut off all systems?
will the key bounce back towards you when you let go, and the jeep will shut down?
it may be your key port, or some wiring in your steering column. pop off the dash and look for any shorted or fouled wiring. if you have access to a voltmeter, test the wires you see for voltage. if you have an alarm system, make sure it is disabled, and the emergency kill is not engaged, it may be trying to kill your systems.