Just swapped a used rear end with the old rear end in a 2005 f350. Everything seemed to be fine until I went to use the four wheel drive. Only tried it in the driveway in first gear, when you take it out of four wheel drive it stays in until you back up a few feet. When I went to push in the clutch you would of thought I stepped on the brakes also, it came to a stop, that's when I knew for sure something wasn't right. The old rear end was 3.73 gears and supposedly the new used rear end is also. I would like to know if I'm missing something, maybe the alignment of the rear axle or something else, thank you in advance for any help!
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There is a good possibility that one rear is of a different ratio.

Count EXACTLY the number of turns the replacement rear driveshaft turns to provide one EXACT revolution of a rear wheel.
That will give you the ratio of that rear..

What was the reason for replacing the original rear ?

 

The spindle was bent. I rotated the tire one full turn and the drive line made right at about 3 3/4 rotations. I assume that would make it 373 gears? If so that's what it had before, this is a one ton, I wouldn't think ford would put any higher of a gear ratio in a one ton. Would it make a difference in the four wheel drive hanging up if one rear end was limited slip and the other wasn't?

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Take that rear driveshaft off and see if you still have the problem.

 

Guess I'm not fully understanding, if I take the rear drive line loose how am I going to tell if the four wheel drive is still binding up?

 

I don't know the answer for sure, but there had to be a reason the original differential bent pieces.and the problem may not be with the differential..