By your description -- what's happening is half of what should be happening. Your headlight should go dim when you press the button, but your starter should also start to turn.
If the starter turns when you jump the posts of the solenoid, then you should suspect the button and do tests to confirm whether it's working or not.
If it doesn't turn when you jump the solenoid, and your battery is fully charged, then you should suspect the wires to the starter or the starter itself.