Would it be better to keep making payments on my totaled car, and use insurance money for a new one?

Question by KiNG*: Would it be better to keep making payments on my totaled car, and use insurance money for a new one?
Here is the situation:

My car was stuck by a semi from the rear, and the truck driver's company who has their own insurance company, has given me a check for the car, claiming it to be totaled.

This is where things get tricky, The company DOES NOT want my totaled car, stating the title will be delivered to the shop or person in possession of the vehicle, who happens to

Car Auto Insurance