Before jumping to any conclusions, why not remove all the terminals one at a time and thoroughly clean them to bright shiny metal. Then reinstall the connection and move to the next until you have every terminal concerning the starting circuit cleaned. Then if you experience any clicks but no start you know it isn't the wires. Start at the battery and clean them first INCLUDING the ground wire.
The starter solenoid is merely a big relay. The small wires going to it are the control voltages. When you turn the key, you apply 12 volts to those wires and that creates a magnetic field that pulls in the heavy contacts allowing huge currents from the battery to be applied to the starter. So it allows small wires to control that huge relay type solenoid. Same setup most every vehicle uses as well. It is called a starter solenoid, but in reality, it is merely a huge current relay. If it weren't for that solenoid, you would have to have a key switch that could carry all the amps the starter needs to start the engine. That would be a monstrous key switch for sure... JMHO
