Damage in a parking

If the operator of the parking facility (which may not be the hotel) and/or the hotel was negligent, you may have a claim against it.  However, your contract with the parking facility (check the writing on the parking claim ticket) almost certainly limits the operator's liability for negligence to a small amount, if anything.  This agreement would not be enforceable if the operator was reckless or grossly negligent, but has a good chance of being enforced if the operator is considered only negligent.  It's hard to set a bright line between negligence and gross negligence, but for example if the operator failed to take steps to rid the space of rats it could possibly be considered negligent, but I don't think grossly negligent; if the operator put the rat into your car as a prank and it got into and damaged the engine, then you might have gross negligence.  Whatever the situation, however, you definitely should raise the issue with the hotel and the parking lot operator.