Help: 95 Cherokee intermittent start problem

My 95 Cherokee has taken to starting when it wants to and not necessarily when I would like it to. Six cylinder, auto with 120,000 miles or so and it runs fine. Lately it will start fine one time and then be dead the next. Battery is fine, starter seems fine, connections and grounding have been checked. When it acts up, gauge lights come on, but there will be no turning over at all -- just that awful, dreadful silence. Can wiggle the switch and steering wheel with no effect, can wiggle the transmission lever with no effect, can rock the Jeep back and forth, with no effect. Sometimes you can get it to start after it refuses to do anything for ten or eleven trys and on the twelfth try it will start right up. Sometimes you can be stranded completely with it refusing to do anything at all. Come back later and it will start right up. I need some ideas --- anybody??? Thanks, Dave