That first image shows the square-drive cable that transfers the motor's power to the opposite side of the seat. It should not be out of its housing like that. It's possible that those vans were travelling at a high rate of speed when they collided, then bounced off the housing, unplugging it in the process. (LOL)
Joking aside, that cable needs to be plugged back in. If the attaching hardware has been broken or damaged, it may need to be replaced.
To get easier access to the underside of the seat, there should be 2 bolts holding down the rear feet. Remove them and then tip the seat forward. You may be able to reattach it yourself, but be aware that you may need to hold your tongue just right now that you've operated it with it unplugged.
I'd suggest that, after getting it plugged back in, you run the seat to its most forward and rearward positions. When one side gets there, the other may be there as well (if you're lucky), or it is still a bit away. What you want is to find the direction where the side that was unplugged reaches its end movement first, then unplug it again, and move the seat the rest of the way there, then plug it back in again.