The problem could be the solenoid, starter motor, battery or connections. The solenoid is energized by the small wire and connects the starter battery terminal to the starter motor. It also engages the starter gear to the fly wheel. Those are the clicks you hear. Also, note the starter's ground connection includes the starter case to engine, engine to chassis, and chassis to battery negative terminal and must carry the same high current as the positive path.

If you can, connect your meter to the starter's battery terminal and the starter case. There should be about 11-12V when the starter cranks the engine or 12V when it does not. The voltage should drop only a little when cranking and indicates a good battery and connections. A full 12V when the starter does not crank may indicate a bad solenoid.