before you go replacing the cylinder and tearing the steering wheel cover off, check the battery and make sure its getting a good charge. I had the same problem, went and bought a new ignition switch thinking that was maybe the problem and installed it and the problem was still there. I had tested the battery prior to doing all this and it seemed to be fine but I tested it again and it was barely holding a charge. So the battery not having enough charge must have had some effect of not activating the solenoid and letting the key come out idk, but it fixed the problem when I replaced the battery.
Of course if your car is starting fine then this probably isn't the problem but give it a try.
