Good luck with that. From what you're describing and without pictures it sounds like you have a broken substrate (screen). Technically it likely wouldn't be covered under warranty.
When you get your new one you'll want to be careful with it. From what I've seen most of the screen breakage of this sort is due to twisting/bending of the frame of the device, which a cover may or may not protect against. This is especially true if you carry it in a briefcase or knapsack. It also may not show up immediately but at some point later. Search the forum here if you want more details or pics of the substrate (extremely thin glass plate that the e-ink uses).