What lovely photos of a solonoid! The quick easy test is to turn on the head lights and then try to crank her. If the headlights go off and all she will do is click then look to the battery connections and the battery itself. If you get her running then turn on the headlights and see if the headlights stay bright.. If so it indicates the alternator is good. For six bucks or so you could purchase a voltmeter at ratshack every grownup with a jeep should own at least ONE of them.
Also most local parts houses will bring their machine into the parking lot and test your system for you--gratis--.
I'd like to see some good photos of the top of your battery. Those could tell us a lot too.
Big Jim <img src="/forums/images/graemlins/kewl.gif" alt="" />