Matt,
I'm very sorry to see this.
.
I had a VERY good experience with UPS damage claim. In my case, the UPS guy left my item on the porch. Then, it rained all day the next day. I called UPS and they had my claim processed in 5 minutes and I had my replacement product on my doorstep in 3 days!
I suggest you calling them and file the claim. Answer any questions they ask you and see where it goes. InfmousAXEL did say that if they deny it, send him the paperwork. He will follow up on it. Personally in my case, no one even came to check my box. They just asked the manufacturer and sent me another identical item. Hopefully everything works out.