This method is sure to work. You will need a small saw blade from a jigsaw, like the one in the picture below. If you can, go for a metal saw blade. The blade needs to be very thin with very fine teeth. Use a pair of pliers to cut the saw blade, so the end also has teeth and isn’t smooth. Make sure there’s a large tooth at the end of the blade.
How does it work
Push the saw blade into the lock with the teeth facing your way. That way, you’ve got something like a little angling rod you can use to angle out the key. Move the saw blade up and down to try and pry out the key. It might take you a few tries, but the broken key will jump right out of the lock.