When I hit the starter button on my '75 FXE with new battery, that I know has a full charge, the relay under the battery clicks but that's all. The solenoid does nothing and the starter does nothing. So I'm going to swap them both out.

Is any one component manufacturer better than another? I tend to be OK paying more for something if I know it is good quality and will deliver long service life.

 

First check/replace the relay.

 

That is certainly a simpler solution. My assumption was that since the relay made a clicking noise, it was working. But that may not be the case at all. Just ordered a Blue Streak, it seems to get good reviews. Thank you for the suggestion.

 

i have the same type of relay on my 85. a ford car relay is the same thing, the ford relay has 2 small studs on it. just use the stud that is in the same position as the harley one. it will work like that.

 

Also check the ground wire to the starter motor.

 

I have a 75 and had all the starter woes. When I did a complete teardown I re-wired the whole bike. Pretty basic wiring. I have the relay that was in it when I bought the bike 20?? years ago, same starter also, gone through a few solenoids, I think the Accell one outlasted the others.
Are you 100% sure your battery is good????
Do you have a meter??? If so trace the voltage. It should go from the battery through the relay, through the solenoid and into the starter with none-minimal voltage drop. When you hit the button.
Check and clean all connections.
You can jump the relay under the seat and see if that kicks the solenoid. You can jump the starter from the positive side of the battery, don't need to worry about the starter ground, is none. It's bolted to the engine.
Clean the handlebar switch, there might be 40yrs of crud in there.