The mower ties to start when I hook up the battery

Inspect the wiring running from the switch, looking for bare spots in the wiring insulation or any type of damage which would allow a positive wire to contact ground. Lawn mowers are subject to a lot of vibration and it's possible that over time, a wire rubbing against the chassis or body of the lawnmower has had the insulation worn to the point that wire is making contact with metal causing the ignition circuit to be closed. If all is in order, there is a short in the ignition switch. A new switch should be available from anybody who carries Craftsman products. Installation is simple requiring nothing more than a pair of pliers to loosen the jam nut on the old switch if it is too tight to remove with your fingers and possibly a screwdriver. In addition most auto parts stores carry a generic style ignition switch which would easily replace the one on your mower. Please don't forget to remove the negative side cable from the battery before you attempt removal and installation of the switch to avoid any arcing and possible damage to your electrical system.