Clean connections and apply dielectric grease to each connection to keep out water and oxygen that will otherwise cause corrosion all too soon. ALL CONNECTIONS, including grounds. The starter solenoid grounds to the starter body, the starter body grounds to the bell housing or transaxle or gearbox. Also one or both of your battery cables could be bad, so buy or borrow different ones to try and see if that makes a difference. If you have any of those "repair" battery clamps that bolt/clamp onto your old battery cables once the old clamp is sawn off. Then get new cable/s. Batteries (unless a sealed battery) sweat out sulfuric acid that gets into any crack of any connection to cause more corrosion. If still no luck take your starter to a local rebuild shop that does starters and generators to have them test it and if need be rebuild it.