When turning the key to start the car it does nothing?

Been having this problem go on for months. go to turn the key and it does not do anything. change battery, already checked relays they good. changed the ignition switch but without the key lock cylinder. so I'm thinking starter solenoid or key cylinder. another thing it goes a month or two without it happening and then it starts again. for some reason I also tried jumping it off another vehicle it didn't do anything still. Yeah, I did this before I actually replaced battery but a jump box will start the car up everytime.