is a business liable for damage to my car when somone broke into it while in their lot?

I would have to some research to confirm it, but it sound like this is what we call a "bailment" situation, and there is responsibility for the theft while in the custody of a commercial business acting on your behalf. You may also have theft coverage, so I would advise you to persue both avenues. You can try to get them to pay on your own, but the services of an attorney could be necessary.

I hope this helps and I wish you good luck in resolving your legal matter.