How to use a Broken Key - something to grip it for one use.

You might be able to retrieve broken part of key. Take a bobby pin or paper clip and straighten, or if you have a scribe.. I will include picture of a scribe. Push the cover of lock cylinder in with scribe,bobby pin or paper clip and make sure you can see the remaining part of your key...if the key is not twisted i would put asmall drop of super glue on the part of key that came out and while holding cover of lock open insert and hold against broken part of key for abt 30 seconds and key should remove with brokenpart attached...if key is twisted, use a small flathead screwdriver to glue to piece of broken key.
Replacing a key is much cheaper and far less time consuming than replacing lock assembly. If you can not get broken part of key out. I will tell you how to replace lock assembly...good luck

use a broken key remover. very cheap tool that comes with
lock pick set. thin metal strip with a hook at the end. fiddly job but it works.
remove broken piece of key then get a duplicate made

Lock smiths have tools that may allow them to remove the broken key without removing lock cylinder.
I have had success removing broken keys by bending a long pin to form a small hook at the end, then using this hook to enter the lock cylinder, hook the key stub in a notch and pull the stub from the lock.
Depending how deep the key stub is, it may be possible to CAREFULLY! apply a drop of Cyanoacrylates glue i.e. "Crazy Glue" to a suitable stick / pin / rod / or the original remaining key, stick it to the broken stub, allow it to harden, and remove the broken key.

They make small lock picks with little hook on the end you can pull the broken key out with .I have seen them on ebay pretty cheap.

Locksmiths use a tool that resembles a thin piece of a coping saw blade. That tool is slid along side the key stub, turned so that the teeth grip the stub, and pulled outward.

They also use a thing that is like a dental pick, only with a smaller hook.

I've heard of supergluing a toothpick (or the other half of the key) to the stub of the key, but you would have to be very, very careful not to get any glue on anything but the end of the broken piece of the key. You also have to be able to hold it long enough for the glue to set.

I've also read that lubricating the key stub and lock with a lock lubricant helps with extraction, but that would clash with the superglue method.

As far as removing the cylinder, it has to be in the 'ACC' position. The only alternative to this is to remove the entire switch assembly and replace it with a new/used unit. This would mean having to add another key to your keyring(s). I believe that removing the steering wheel is necessary (or very helpful) when replacing the switch on that car.

Good luck from Detroit, MI.

it almost sounds like the lock to latch linkage is disconnected or broken -- or the latch itself is broken(?),, but I can't imagine both of them being broke :-( --- what is the temperature of where you are right now ? is it super cold ?? ( the latches could be frozen up ).
the only thing that I could think of doing is slim Jimming the door open --- the inside linkage control rods run horizontally from the door latch to the inside lock/unlock lever,, if you can make a 'L' shaped tool out of some stiff wire and put a small gripping bend in the lower end to grip the linkage -- you might be able to wedge a gap between the window and door ( using wooden wedges ),, you might be able to grab the linkage and get the Jeep to unlock.. now if you do not want to take the chance of breaking the window or you do not have a stiff enough wire to do the job --- I would just pay a locksmith the 45 dollars too come out and open the Jeep,, and then when you get the doors open I would pull the inside panels and fix the linkage/latch problems.
and now that I think about it --- does your Jeep not have a rear door that works with a key ?? if it does,, just get in that way and unlock the doors manually and then fix the problem.

c...

you might be able to put a very thin coat of super glue on the end of the key piece you have in your hand and then hold it against the broken part unti it sets. Be careful not to get it on the lock cylinder. If the key broke off in the ignition cylinder, you should be able to turn the lock cylinder the start an run positions.

Or, is it not all the way in?

What make, model & year?

let me sugges that you first spray plenty of lubricant down the key slot. Get a small pair of vice-grips & lock onto the inserted key. Use any screwdriver, or other tool that will lay between the vice grips & the cylinder and use a leveraging motion with the vice-grips to easily extract the key. Your vice-grips would be at a 90 to the key & hopefully you can grip just below any plastic area. Stick something through the hole & grip below there & pry. You shouldn't have to actually do more than leverage the key out & since it went in, it shouldn't harm anything. Make sure the key hasn't been turned in any direction first and is in the off position. Good Luck & hopefully this will save you some time.

Try spraying some type of lubricant like wd40 in the key hole and using a small metal pick to dig the broken part out. You can also use skinny flat piece of metal like a nail file and place a strong magnet on the end of it with any luck it will grab the broken piece of key. Good Luck