Use your wifes tooth brush. Just remember to put it back. Actually for the springs try a foaming cleaner with the wife's toothbrush just remember to rise it first befire you put it back
Check all of the connections and starter solenoid. If it's only clicking sounds like solenoid but do a check on the voltage in the battery. Just cause it's a new battery could be down in voltage...try jumping it if goes on a jump then the battery is low if it just clicks start checking wiring...