Something is not connected properly then.
1/ Car switched off, on the ground try turning the spur by hand. Does it move the car? If you hold the car back resisting the drive is something slipping?
as mentioned above, no it doesn't
2/ If it is slipping somewhere try turning the layshaft with a nut driver on the slipper nut to rule out the slipper and see if you get drive.
Turns ok, cant see an issue there
3/ If no to the above, check the gearbox gears are not stripped
Gears look fine to me, see pics
4/ If OK check the wheels are on correctly with the drive pins in place and the hexes are not stripped
Checked drive pins and hexes, look fine to me, see pics
5/ If all the above checks out it is definitely the diff. You should be able to tighten it so you can't tighten it anymore, if you can't then the nut maybe stripped of the internals are not correctly built.
Read the big thread on here about the diff, it mentions using the B4 diff screw instead as apparently that's better, is that the best thing to try? I assume its this one
http://www.ebay.co.uk/itm/2721446223...%3AMEBIDX%3AIT
6/ It sounds like you have a second car. Try swapping the working diff into this car to confirm the rest works.
7/ Compare the two diffs but I can understand you not wanting to strip the working one down.
Take lots of pictures and post them on here.