All clutch-style and Torsen-style limited slip differentials have to have the clutches preloaded in order to engage and hold. This is done by simply stepping on the brake while applying throttle.
If you are starting on a surface other than wet ice, and the differential is the Auburn design (5 coil springs in the center), then the differential is nearly worn out. When this happens the clutch cones wear to the point that the oil channels are gone and the cone is bottomed in the case. With no oil channels, the cone will ride on a film of oil and not grab. If its the older (pre-'92?) split case design, its sometimes possible to machine the small face of the cone ~0.020" and shim the differential gears to restore limited slip functionality for a while. You can hand-file the oil channels to make them deeper. If its the newer end plug housing, its not repairable.
The Torsen (all gear) limited slip has no preload of its own. With one wheel on ice, it will behave like an open differential until preload is applied with the brake.
The disc clutch style units (TracLok, etc) use Belleville springs in the clutch pack to apply some preload. If the clutches are worn (very rare), they will slip until preloaded with the brake. The clutch packs can be replaced. A special tool is required to compress the clutch packs so the pinion gears can be rotated into the case.
Ken
