I can't speak for non-US cars, but most of the US car require the key to be in the lock to remove the cylinder from the switch assembly. You can trip them to release them, but without the key, nothing will happen.
If you have the portion of the broken key that allows the cylinder to be used, try to put it into the cylinder and then release whatever you're doing to release it.
Other than that, good luck and maybe someone else will chime in with an actual correct suggestion.
Stay safe and healthy!
