I have a Snapper LT12 that just clicks when I try to start it. Put a new batery in with same results. What else could it be?

Check to make sure the PTO is off, brake is applied, and your butt is planted in the seat. If all above is met, and battery connections are clean and tight, the starter solenoid is suspect.
Follow the red wire from the battery to find the solenoid. Jumping across the top two terminals should spin the engine... MAKE SURE IT IS OUT OF GEAR AND BLADES ARE OFF!

If it turns over, solenoid is probably bad.

Best of luck,
Victor