If I was closer we could have a beer and chase it down. Use the search and start reading on YJ won't start threads. If you know anything about wiring here is the start circuit. I know it is a 93 diagram but should help.
Like joker said, look around and you will find a lot of good info.
Before you do anything else, put the battery on a charger overnight and while it is charging, go thru all of your connections positive and ground. take them all loose, clean them all and use some diaelectric (sp) grease when you put them back together. Pay attention to your grounds, make sure all are clean and tight.
Replace any old or correded cables with new and you will more then likely find your problem. Remember, just because the lights come on does NOT mean the battery has a good enough charge to start the jeep.
It's funny, my 91 Islander did the same thing to me. Turn the key, click. Battery is good, even tried giving a boost, click. I checked solenoid, connections, click. I was underneath the engine, wiggled any wires I could see, she turned over. I need to figure this out. Maybe a bare wire somewhere??
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