I think ups denies all claims at first, with damage, in hopes that you wont persue it but dont be fooled. You have a lot of options.
First of all they have a legal responsibility to cover something because there is a implied warrenty to get it there in one piece nevr mind after adding insurance.
Call and push them. If they deny you ask to contest it.
If you get to impatient call your local Attourney generals offce. Information will have the number and this is a goverment organization designed to help people in your exact situation. They do this for free, are familiar with all the local laws, and will tell you all your legal rights and what you can do about it.
You can also call the better business burue and from there you can call both agencies in the area that the ups main office resides in.
Dont be intimidated by ups and call these agencies.