Hi there,
Yup, it sounds like your cable is indeed broken somewhere in the housing. You should be able to pull the cable out of the housing, and it shouldn't have any kinks or worn spots in it. If it has broken, chances are good it has damaged the housing at that point, but you could check the outer portion of the housing to see - just measure in as far as the broken piece would go and see if there's any signs of a problem showing on the outer cover. Probably the easiest and cheapest fix would be to go to a wrecking yard and get another cable and housing to replace yours with, or order one from the source on this board.

Good luck with it!

Richard Wooldridge
'82 300D/4.3L V6