Clicking/Popping Transfer Case.

I've got a 4x4 2nd gen that has a really weird problem I haven't seen posted before. When I'm going up hills or uneven roads I get a popping/clicking noise from the vehicle's center. I traced it down to the flange where the rear driveshaft meets with the transfer case. You can replicate it with a fat dude bouncing up and down on the bumper. Seems the flange goes in and out very slightly (only a few MM) and it makes a clunk. 4x4 has also stopped working recently. I'm fairly good with mechanics, and could probably take the whole truck apart in a day, but I know nothing about transfer cases. All U-joints are good, so it's not one of those. Have any of you guys heard of similar problems? Or have any advice on how to tackle it?