Okay - lots of guessing

The thing that seems to take a symptoms would be something binding the 4wheel shift mechanism - if you're at the point of parking in snow - I'd look for ice/snow binding something somewhere, preventing full gear engagement/disengagement.

other things - if you get snow stuck on a wheel (or ice - snow melts as you're driving - freezes when stopped) it might be enough to through things out of balance.

The clicking stops on braking worries me a bit - that sounds like loose wheel lugs being centered by the brake - doesn't fit with the 4wd mechanism - but doesn't hurt to check torque.

also on the acceleration doesn't change pace - is it wheel speed? or engine speed?

So is something keeping it from moving thus making it die or are they two different problems?

Sounds like something is up with the brakes if it stops when you touch the pedal. Maybe a bad caliper or a bolt missing from a caliper.

I had a bad clicking noise from my front right wheel when I turned left. I could actually feel it from my seat. I took the caliper and rotor off, checked the bearings, put it all back together and made sure everything was torqued. Ive not heard it again and that was over 2 months ago.

I also saw that Uffe said he changes into 4-lo in P (park) most the time. I would not recommend this at all and I'm not even sure how it's possible. The transmission needs to be in Neutral, end of story, for you to be able to mechanically lock the axles (what happens in 4-lo).

It's winter and I've been using full-time pretty often. I've used 4-Lo twice, to relieve myself off a snowbank I had to park in (on the street, narrow road, I pulled up onto the snow bank a little).

One time when I used for low, it make a wierd clicking noise and no movement. I shifted into 4lo in neutral, like your supposed to and gently pressed to gas to creep out of the snow, when it make the clicking sound. I would best describe it as when you put baseball cards in your bike spokes.

I put the Jeep back into neutral, shift back to fulltime, then back into 4lo and it works fine and I crawl out of the snow.

Now, whenever I go 30-40 mph I hear a similar clicking noise...buts it's more spread out like a horse galloping. Anyone have any idea what this is? Acceleration doesn't change the pace at all, but braking stops it. It has no negative effect on the ride at all, but I figure something is about to give. I've tried all 4wd systems and they all work fine.

You shouldn't be able to get into 4-lo unless you put the auto tranny into N. That has been my experience, and that's what every manual says on how to shift into 4-lo (and 4-lo only). I've also forgotten to do that once when trying to shift into 4-lo, and it wouldn't allow me to fully shift into the 4-lo position. 4-hi (part-time and full-time if you have the Select-Trac like I do) can be shifted into at any time you are traveling below 55 MPH. Unless maybe you have a manual transmission, this should be true for you, too.

If I brake and put the tranny in neutral and attempt to shift into 4LO I get the gear teeth churning.

My manual says I should not change to 4LO while my transmission is in neutral and the vehicle is standing still. If this is what happens I should stop the engine, change to 4LO and start back up.

Just use Park instead of shutting down the beast. That way you can be sure there is no problem with gear teeth churning because you lock your driveshaft out of the transmission!

If I brake and put the tranny in neutral and attempt to shift into 4LO I get the gear teeth churning.

My manual says I should not change to 4LO while my transmission is in neutral and the vehicle is standing still. If this is what happens I should stop the engine, change to 4LO and start back up.

Just use Park instead of shutting down the beast. That way you can be sure there is no problem with gear teeth churning because you lock your driveshaft out of the transmission!