There was a recent updating of a posting by I think a member called Dudesky, in which he outlined a number of things to note about the E36, which shares the same 6-cylinder powertrain as the E34. I quote: "Differential clutch pack retaining ring bolts can loosen or back out, eventually resulting in rear end failure. If you hear a ticking noise in the rear, have the final drive checked out."
I have no idea what that means, but it may be related to what you're experiencing.
You're right, this car probably had a tough previous life, one thing one needs to watch out for, unfortunately these cars can invite a lot of abuse and neglect of proper service and maintenance.