If it were me, I would take a voltmeter and see where I am losing voltage before I just started changing things. If you have voltage through the switch when you press it, then go to the next point and see if it is there. If you have it at one side of the relay and not the other then the relay winding is open. If you measure on the contact of the relay that feeds voltage to your solenoid you can tell if it is operating or not. Or you can go to the solenoid input and measure there and it will tell you if the relay operated. A remote starter button is also an easy way to check the solenoid and starter.
Ron