¿From the facts of my case, do I qualify to receive punitive or exemplary damages?

On April 20, 2013, I went to a function at the Marriott Hotel (downtown Atlanta) and obtained valet parking around 6:30 pm. After the function, around 10 pm, I presented the parking cashier with my parking ticket for my vehicle. After waiting several minutes, a parking attendant finally presented my car and proceeded to tell me that they had a "small accident" in my car. He showed me the damage and to my surprise, the front corner driver-side panel was torn off the vehicle. Although, the parking attendant drove my car, he failed to tell me that the car was not drivable. When I tried to drive home my car was too damaged to operate. Suffice it to say that what was supposed to be special extraordinary care for my vehicle (Valet parking), resulted in my car being damage beyond repair. I believe only excessive speed caused the damage to my vehicle. Due to AAA's staff's gross negligence, my SUV received damage well beyond what the company's insurance is willing to pay. I am terribly inconvenienced by the total loss of my vehicle, which is causing me much stress, loss of hours from work and numerous telephone calls.