I'm going to go on a whim here and propose this hypothesis: is it possible that the car was a perk of one of your Sim's old job? A few career paths come with free car perks, the obvious being the patrol car for law enforcement and the firetruck for firefighters. I think the investigators eventually get a car too.
I had this happen to me last night on a Sim who was level 10 firefighter. Quit his job and the firetruck in his inventory got stuck, couldn't drag it at all. I'm having a mind blank on what happened next (this is what happens when I play late at night), but one of the following two things allowed me to drag it again. He used the truck to go somewhere and parked it on his own in its garage spot, after which I could drag it around; or joining the firefighting profession again, at a lower level, made it unlock.
So perhaps you can try both those things. Forcing him to use the car and park it, or see in his career history if any of his old jobs could have given him a work car.