I had a FEDEX issue in 2006, they delivered to the wrong address and refused to honor the insurance claim. I gave them the slip you write out in the store, the employee typed a completely different address in their system.
Their MO is to deny, deny, deny and hope you go away. If it is FEDEX, and not the recipient, then I would claim through the local court system - in my case it was the magistrate court local to the FEDEX office I used. I had the evidence that I submitted with the claim. My expectation was that they wouldn't send an attorney to the court, too expensive, and as most customers give up they've factored in that the tenacious ones will pursue them and they'll settle before the court date. This is what happened in my case, I received a call from a legal secretary in the regional office - she tried to negotiate the claim down, I refused to budge and told her I'd see them at the hearing. This triggered them to pay in full.
I posted my experience in the GR Research circle, if you search under my user name and FEDEX it has what happened in chronological order.
Good luck!