The garage certainly has a 'duty of care' in respect of your vehicle but, in order to successfully sue them for compensation for damage to your car, you'd have to show that they breached that duty of care through their negligence. If the car had been stolen because they'd left the keys in the ignition, they'd be responsible because you suffered loss through their negligence. However, there's nothing in your post to suggest that they've been negligent, so there's no reason why they can be made to pay compensation.
Try looking at an analogy. Let's suppose that your boss asked you take a large amount of cash to the bank for him. You'd obviously have a duty of care not to flash the money about in the street, or to leave it on a bus, but do you think it would be reasonable for your boss to expect you to repay the money if, having taken all reasonable precautions, you were mugged on the way to the bank? You wouldn't be responsible for the loss, so there's no reason why you should pay compensation. The garage wasn't responsible for the damage to your car, so there's no reason for them to pay you.
Chris