Do you have the receipt? End of problem - tell the valet company you will report a theft of your car (given you have been deprived of the use of your automobile, and it was turned over to the custody of the valet company representative as evidenced by your receipt) if they do not make it right - either by finding the keys or having keys made at a nearby dealer, forthwith. Then they can deal with the authorities (they must have a central office / HQ with managers with more teeth than the onsite idiots).

But you do have a major problem - the valet is a contractor, and I am pretty sure there is a hold harmless clause at work here - the hotel is pretty much not at blame here, the valet is. They may compensate you for some troubles at the restaurant and for the trouble caused by their contractor, but...