If my car was totaled at the shop while being repaired, who is liable me or the shop owner?

The repair shop is liable for negligence for the damage to your car.  Your claim should be filed with the repair shop's insurance carrier.  If the case is not settled with the repair shop's insurance carrier, you will need to sue the repair shop for negligence.  Negligence is the failure to exercise due care (that degree of care that in this case a reasonable auto repair shop would have exercised under the same or similar circumstances to prevent foreseeable harm).

In order to prove negligence, you will need to prove duty (of due care) discussed above, breach of duty (failure to exercise due care resulting in the damage to your car), actual cause, proximate cause and damages.

Actual cause means but for the repair shop would your car have been damaged?  If the answer is no, which appears to be the case, actual cause has been established.  Proximate cause means were there any unforeseeable, intervening acts which would relieve the repair shop of liability?  If the answer is no, proximate cause has been established.  Damages means the amount of compensation you are seeking in your lawsuit for the loss of your car.

If the case is settled with the repair shop's insurance carrier, NO lawsuit is filed.  If the case is NOT settled with the repair shop's insurance carrier, you will need to file your lawsuit for negligence against the repair shop prior to the expiration of the applicable statute of limitations or you will lose your rights forever in the matter.