Florida lawyer here and this issue happened to me last year at the Four Points in Miami Beach. Only difference was it was my personal car.

I got a major runaround from the valet manager and staff. So I needed to get the general manager of the hotel on the phone before I got a resolution. You have to be persistent and professional. The GM will be professional, the minimum wage valet an his his/her $1/hour + manager will not.

If you can't get the GM on the phone, figure out who the owner is and call the owner's attorney - not hard to figure out. They are going to want to pay you quickly and not have to pay their lawyer to deal with it.

Take pictures of the damage, if you can.