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Does the key turn to the full OFF position?
Does the key start the engine?
No the key does not turn to the full OFF position.
Yes the key will start the car.
The most common problem is a faulty ignition key lock cylinder. The tumblers that allow the lock to rotate when properly positioned by the key can stick and not allow for full lock cylinder rotation. Many times, it is possible to spray a lubricant into the lock, tap on the key and jiggle the cylinder to the OFF position.
Another possibility is that the sensor at the shifter is not registering PARK. When the vehicle is not placed in PARK, the key will not come out for safety reasons.
Additionally, it is MOST common for the mechanism in the lock cylinder assembly that releases once the vehicle is placed in PARK to stick. Again, lubing and tapping the key usually gives it one last removal.
If all fails... Unfortunately the ignition tumbler will have to be replaced and the tumblers keyed so your current key can be used. If the solenoid which is near the shifter has failed, then it will need to be replaced.
A mobile lock smith will be a much less expensive repair and can have this repaired in about one hour.