Are you absolutely positively 100% sure that the positive battery cable is connected at both ends?

You hear the solenoid clicking which means the control side works fine, you need to focus on the insulated side of the starter circuit or the starter itself.

Most starters have some sort of jumper between the motor terminal on the solenoid and the motor battery terminal. Inspect the wire and make sure it is not disconnected.

With the headlights turned on, crank the engine over. Take note of the decrease in brightness. Refer to it as the poor mans battery tester.