I have a Honda 3011 which doesn't fully charge the battery so I've been jump starting between mows. All of a sudden I can't even jump it. It's like a kill switch is stuck open as I don't even hear the clicking you'd normally hear if the battery was to low to drive the starter. Any ideas?

Are you sure that the battery is bad. The 3011 mower has an issue with the control box that will act like a dead battery. Try pushing on the center of the control box(Square box behind the battery) while turning the key.