BMW Repair: 1987 BMW 325, limited slip differential, 1987 bmw 325

Question
I have a 5 speed transmission. For a while I have noticed a noise and slight shaking coming from the car when I accelerate. It got worse and worse until yesterday something went out and went out loud. I tried to tow the car but the rear end was locked up. I can move my shifter knob into different gears fine I think. The rear end released and I was able to be pulled a little ways and I was in neutral with the clutch pushed in and I can still hear the noise and grinding. Then the wheels locked up again and I wasnt' able to free it. Is this my "rear end" or my transmission. And how much roughly or is it worth fixing. Thanks.

Answer
Micheal,
 I cant tell you if its the rear end or not, thats what you'll have to figure out.  You can raise the car and grab the driveshaft and see if it will turn.  I'm assuming it wont, so try to figure out which end of the driveshaft is holding stopping it from turning.  One end of the driveshaft goes to the tranny and one goes to the diff.  If the diff end feels stiff but you can get some play out of the other end, then the diff is likely the problem.
 Also if you raise the rear of the car you should be able to spin one wheel forward or backward.  If the wheels wont spin its probably the diff, or you have a limited slip differential and its normal.  So there's no easy way to tell unless you remove the driveshaft from the diff.  With the driveshaft off the diff, you can spin the pinion and if it's free, then it's definately a tranny problem.  and vice versa.  Try to spin the driveshaft while the tranny is in neutral, if it spins then the problem is in the diff!
 Hope this helps,
 Josh