I have an '03 GSR and I'm having some rear LSD troubles. Just over a mile from home, I heard clicking from the rear of the car while accelerating or holding a constant throttle (not while off throttle, in or out of gear). The rear of the car actually shook violently at one point, and I quickly pulled over to check it out. When I started moving again, only the clicking happened again until I got home - a total of a couple miles. The clicking occurs while going straight and turning, it doesn't seem to matter.
With the car in the air, if I manually turn the rear wheels, in or out of gear, no clicking occurs. So, I got an effective, but less than brilliant idea. I had a friend run the car and slowly let out the clutch. No clicking. If we applied the brakes, the clicking happen intermittently, but loudly. I'm 99.99% sure it's the diff, but I'm obviously no expert.

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Here's what I'm seeing with the car off the ground:
When it's in gear, if I manually turn the rear, the fronts do not turn, but the opposite rear turns the opposite direction. If I turn the fronts, the rears do not turn at all.
When it's in neutral and I turn the rear, the fronts turn a slight bit just when I start to turn the rear, but do not continue to turn when I keep turning the rears. When I turn the front (in neutral), the rear turns very slowly. In either case (neutral or in gear), I only turn the wheel about an inch before the opposite side begins to turn. When I turn the car on and let out the clutch, all wheels turn with no detectable hesitation. Again, the sound seemed like it was coming completely from the rear.
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So, does anyone have any ideas? Might it be something other than the diff? (Again, I'm no expert). Any help would be much appreciated.
Thanks!