A Limmited Slip Differential Question

The limited slip function is malfunctioning, because the clutches are burned up from allowing one wheel to spin while the other is at rest. They can stand it some, but doing it over and over and over again, like dropping off the pavement coming up your driveway wore it out. It's time to rebuild or replace it.
I've only lived in this house since 2017 and the truck remains parked all winter. I've had to drive around another car to park up by the garage a total of three times, and each time it got stuck. Prior to that the truck was only driven on the streets of Los Angeles, so while burned up clutches as you describe may very well be causing the problem, I'd be surprised if it happened here in Pittsburgh. But this brings up another thought. The truck was rear ended while parked on the street in Burbank one night. It was hit hard enough that it was launched into the Mercedes parked in front of it, which was in turn launched into the SUV parked in front of it. Both of those vehicles were totaled. Could an impact like that have damaged the differential? The truck in question is posted below. And thanks to everyone that's offered advice. I appreciate the time you took to comment.
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