If both wheels turn and the ring gear isn't turning either the differential is trashed or the spider gears are missing. You did put the cross-shaft back in, right? If you turn one wheel and the other goes the opposite direction, that's normal. The clicking could be the governor turning - I can't remember if it makes any noise or not - or it could be in the clutch packs. If you didn't put the bolt back in the cross shaft it could be wedged against something preventing the the ring gear (and carrier) from turning.
You haven't driven on it, right?
Working on a differential is a slippery slope. The difficulty with setting pinion preload is that the spec only applies when when there is no ring gear, meaning you have to take the axleshafts back out and pull the whole carrier (taking careful note of the position of each shim). Then you need to make sure the backlash is still OK and really the whole pattern. If something isn't right you're doing a whole gear setup. On a high-mile diff it's sometimes best to just get the crush sleeve back exactly how it came out and not worry about how the parameters have changed with wear (unless something is obviously wrong). Some people have good luck re-using the crush sleeve by controlling the pinion nut torque carefully (so as to not further crush the sleeve) and stake the pinion nut in place when done. Or the crush-sleeve eliminator could be used for that. Ideally you would have measured backlash before you took it apart, but it's probably too late for that.
