Turkish Airlines complaint: Suitcase broken into, ruined and customer service ignoring my complaint

I flew business class with Turkish Air from France to Turkey and on to Singapore and Australia. I got home (after a 40 hour trip) and when I went to unpack my case I saw that the zip had been cut with a knife, the zipper taken off and my case open and gone through. It was then rezipped carefully as to not expose the damage. Turkish Air are telling me that my case is not valid as I left the airport without reporting it.

The fact was I couldn’t see it until I went to unzip it and the zip fell off and I saw it had been carefully cut. The suitcase is a Samsonite $1,049 case and ruined as you can’t replace the zip on them.

After 20 messages arguing with them, they offered me $20, which I declined and told them it was not enough and clearly they recognise their liability.

Each message I send to them I ask for:
1. A replacement case;
2. A contact so I can lodge a formal complaint about their customer service;
3. My case to be escalated;
4. A call or the details of a senior manager.

Turkish Air now just ignore my messages.

I am so angry that their marketing department paint a picture to convince us we will be treated in a certain way and yet they treat us like animals.