Sounds horribly like you need to get your hands dirty.
The LSD is behaving like an ordinary one.......both wheels should definately spin together if it was working ok. For the amount they cost they should work until the end of time, but sometimes you're unlucky.
It could just be that the clutches are worn, but the diff will need to come apart to be sure.
Start giving-up something now, that way, when the bill comes in you'll have some cash towards it..........
'73 Jensen Interceptor (Resting)
Giant Full Sus Mountain Bike