Same thing happened to me with our front door years ago - I now really understand the concept of 'metal fatigue', because it was totally obvious that that was why the key broke - it just twisted apart in my hand along the stress lines. Anyway, we had to get a locksmith to come and take the lock out of the door, and take it apart to get the key out. Good luck.
Take a piece of wire, such as coat hanger size, maybe 5 inches long, creat a point at one end. Hold with insulated pliers so that the point only touches the end of the broke key, arc with a positive wire from the battery to the other end of the stiff wire. This should creat a mini weld between the key end and the held wire. Pull very gently.
Look in the owners manual and see if the key numbers are written in there. With the numbers in hand you can go to a Chevrolet Dealership and they can make the key for you there. They say the dealership can look up the key numbers with cars VIN # too. I'd get the VIN # and call the nearest Chevy dealership to see if they can help you.
I tried getting a new key cut at the dealer - they told me they don't use the VIN but if you still have the metal tag the keys came with it has an identification number. I don't know if this is only true for older cars like mine.
See if you can remove the back seat and gain access to your trunk that way. Then open the trunk lid to remove lock cylinder, very difficult to do from the outside without doing a lot of damage. Most keys are brass and you will only create more problems if you try to "weld" it.
I worked as a locksmith some years ago. To remove a broken key we took an old hacksaw blade and ground it down so it had a thin section with the teeth facing you as you held it. You could then try to slip the thin part over the top of the broken piece of key and rake it out. Once you moved it a little you could grab it with pliers. If this fails use your button and then remove the trunk lock cyl. A locksmith can remove the key and make another one.
You won't believe this - the ignition broke - but got it out. Then I found a trunk key - spare - so I put it all in a bag and gave it to my chevy dealer - and he made keys. I'm trying them tonight. Still have to get the trunk key out...
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