Looking at your window sticker, you don't have a LSD. It says "All season traction (ASC+T)" which is traction control. You would need "Locking Differential" on your window sticker to have a LSD. '96 was the last year that ASC wasn't standard and you could still order a LSD. Still, not many cars came with it.
Your car is very similar to mine. I also have a 96 sport model and my only option is the HiFi stereo system. No LSD in mine either, though I really want one for autox. __________________ 
2000 M5 -> 1996 318ti -> 1997 328i 
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