So is it the solenoid or the power to it? Get across the small terminals on the solenoid and flip the switch. If you get no 12v you have a supply problem. If you get 12v time for a new solenoid.
Some times I have bypassed the solenoid to ensure that its the problem, being internal or supply. I take a pair of common pliers, turn them around so that the handles are sticking out and put them across the 3/8" terminals....expect a spark doing this. If the starter spins trying to start the engine, or if it starts, that ensures your problem is the solenoid or supply voltage.
Something else you could do, if the jumper test works, while you have the pliers handy, select the small terminal with the colored wire....yellow/red stripe I think.....jump from the input 3/8" post to the small terminal with the colored wire. If the starter spins you have a supply problem.....otherwise internal problem with the solenoid.
The solenoid can have 2 internal problems: 1, the solenoid is old and even though you hear a click, the contacts are pitted reducing the cross sectional area and therefore is incapable of suppling the necessary current to spin the starter. 2, The internal coil (small terminals) that when energized, causes the contacts to close is broken...open wire.