Central Parking Services CPS Destroyed my engine and fails to accept liability Hoboken, New Jersey

I drove my car into their lot and left it with a valet.  Upon returning 5 hours later I was told that my car would not start.  After towing it to a dealer and having the engine examined it was determined that the engine was over-revved causing a piston to basically explode.  This diagnosis was confirmed by an insurance examiner as well as a forensic engineering company.  They all also state there were no maintenance issues with the engine.  

I have attempted to file a claim with the lot three times, each time they claim that it was either not their fault or not their responsibility.  They claim they just parked the car and with would not start.  The damage would have been very evident to the driver of the car, and it never run after.  The last time I spoke to someone at the company they told me they spoke to an expert and what I claim is impossible.  I offered to have them examine the engine, but they declined.

It is the local operations manager of this national company who makes claim decisions.  I wonder if their compensation is somehow based on the profit or loss of their individual location and how that factors into their decision.  How many other people are in similar situations across the country with this company?

Details are below on my website