Click, no crank, and the lights dim when you turn the key? Sounds like the motor is locked up- have you considered that possibility? Try turning it over with a breaker bar at the crank pulley. If the motor is not locked up, then it is probably your starter because the dimming lights is proof that the starter is getting power like it should.
I've had bad starters that click but don't turn the engine over, but it was because the wire was frayed between the solenoid and the motor. Therefore, the lights didn't dim because there was no significant amp draw. Also had one where nothing at all happened when i turned the key- not even a click. Had a sticky solenoid that did not want to engage. A few gentle taps with a small hammer and it started right up.
Had an engine that blew up while running (6.2 diesel)- loud crunch. When I turned the key on that one, the lights would dim and the engine would not turn at all. Even if your engine did not blow up, it is still a possibility that it overheated/ran low on oil without you realizing (maybe a bad temp gage?) and seized when it was shut off. If you can't find an obvious problem with the starting system, I'd recommend verifying that the engine turns over by hand before buying a new starter. Also, load test battery as others have said.