Well, I think there is still some "action" going on in the rings. Even if everything in there would be totally synchronized with no relative motion (especially then) you would get mass clumps of particles slowly being drawn toward each other by their own mass/gravity. Basically the same thing that led to planets forming from rings of particles in the early solar system. But then this would be extremely interesting to research, because it would be the nearest thing to look at for such processes.
It would be wise to use a somewhat rugged probe with nuclear power (no fragile solar panels) with some shielding, retractable instruments and an ion drive... Anyway, there are lots of cool things to explore left in the solar system and the closer you look the more interesting things you find!