door handle stopped working yesterday
So if I read this correctly, pushing the button does move the rod just not quite far enough.
If that's the case there is adjustment. Find a small hole in the end of the door. Allen hex key through there to loosen set screw adjust linkage retighten.
This shouldn't have happened suddenly though. You would have been pushing the button pretty deep to get the latch to release for a long while before it went inop'.
Does the button stick in the pushed position?