It sounds like you have an open differential.

Jack up one rear wheel and DOUBLE CHOCK the opposite front wheel. Release the parking brake and place the transmission in neutral.

Use a torque wrench on the lug nut with the lever on a radial line and see how much torque it takes to break away. A serviceable limited slip should require at least 40 lb-ft.

If you can turn it by hand, it's probably an open diff.

Clutch and cone type limited slips diffs require a "friction modifier" additive to prevent clutch chatter. GM and Ford dealers sell this additive in four ounce bottles for addition to conventional SAE 80W-90 GL-5 gear oil.

Duke