riding lawn mower has a good battery but willnot do a thing?

Check all connections from battery to accessories--INCLUDING NEG CONNECTIONS. The frame is the NEG (or some call it ground) This is equally important as the POS connections. There must be a complete circuit for things to work. Rust in between body parts will act as an insulator, and not permit current to flow.
This happens when you rebuild anything, and paint all areas. You must have bare metal to bare metal to complete a NEG circuit back to battery. Use silicon di-electric grease in all connections including frame metal to metal (get it at auto parts store)
Use a test light or multimeter to check continuity from battery to each frame (body) part. You can also add a NEG wire(s) from battery to accessories to make sure you have a good NEG connection

Robert Brown
August 2008