Couple of things cause that. Usually it's a battery that won't supply the 150 amps, give or take depending on engine size, it takes to roll the engine. You solved that problem. My experience with marine engines says you need right at 10v at the starter terminal to case to produce adequate torque to spin your engine fast enough to start (200 rpm). Next at 150 amps and a 12v-10v (for reference), you have a max of 2v you can loose in your wiring and solenoid internal contact. 2/150 = 0.013 Ohms. An Ohm (1) is defined as the resistance that would cause a 1 volt drop across it if 1 ampere (coulomb per second) were flowing through it.....so much for the gobbledegoop!
Clean up your wiring between the battery and engine. That's remove all connections and shine the mating surfaces and put them back nice and tight (considering the size of the hardware....don't need to over do it, just don't want anything loose). If you have been trying to start your engine, the culprit usually can be found by feeling for hot spots at terminals. The heat is where your power is going that should be going to your starter. I liked to use the spray battery terminal coating on all my marine connections after cleaning.
The solenoid is your high current switch that applies battery voltage to your starter. It is energized by a low current signal that is applied across the two small terminals on the solenoid. The Ignition switch applies the voltage but the voltage comes from the solenoid input terminal where all the red wires are connected. If the voltage to the engine, aka that terminal voltage, drops because when you try to start the voltage drops, your starting relay will drop out. Dropping out relieves the load on the terminal and it returns to full battery voltage which re energizes the solenoid, putting the load back on the line dropping the voltage the solenoid drops out etc. etc. etc. That's the clicking noise you hear.
Windy but now you know how it all works. Knowing the pieces to the puzzle lets you solve it.....works for me. Good luck.
