When the caulking in the cartridge is still soft enough to squeeze the outside of the tube but all hardened up in the tip, try using your electric drill to cut a passageway through to the sill soft stuff. If the hard stuff doesn't go too far for your drill to reach, or the nozzle is not cracked (which will cause the drill to simply slip off to the side), you should succeed.
One catch is that one year old caulking is beyond the normal shelf life for most caulking and it may not stick well to the house.