You're certainly entitled to think that, but Dell is going to point you toward the shipping company, which will require evidence (the packaging) that the system was damaged in transit (which it almost certainly was). The system warranty does not cover damage, but the shipper's insurance should.  You would have a more solid case if the damage had been reported on arrival or shortly thereafter.  At this point you may not have a chance with them, but it's your best  option. The system warranty does not cover accidental damage such as a cracked screen -- no manufacturer's warranty on a mobile device does.  
I received my Vostro 5620 laptop 3 months ago. I got it for my wife birthday which just passed. When I opened the box and plugged the computer in, the LCD had a huge crack down the middle of the screen! The box was partially damaged and I suspect the shipping company. I tried calling Dell support and technical support and they keep rerouting me and saying they can't help me. I went through online support to tell them my computer was broken on arrival but haven't gotten any word back yet. I don't know what to do here? A brand new system that is now practically useless, and Dell isn't giving me any help! And what do I do with my broken laptop? All I have right now is a brand new $1200 paperweight.
Vostro 5620, LCD screen cracked, box damaged