I got out my Troy Bilt Pony Riding Mower today to cut the grass for the first time this Spring and it wouldn't do anything when I turned the key. I bought a new battery and installed it and then it just clicked when I tried to start the mower. I replaced the spark plug and it still doesn't start. Any suggestions?

If the battery is new and full charge then I would think the solenoid may be bad here. Check and make sure starter connections ( cables ) are good.

Spark plug has nothing to do with turning over the engine.

Basically its

Battery

Ignition switch

Solenoid

Starter

In that order