I just got Dead Island working on my machine (a small miracle, considering how many bugs are in the game itself.)
I played through the first part where you wake up, walk around, fall down the elevator, and get chased by zombies into the storage room place. I get hit by the zombie, the game cuts out.
The next level (mentioned in the title) starts loading (it takes around 5 minutes.) Once it loads, all I can see is what looks like the sky and some black squares & rectangles above me (I'm guessing they're supposed to be buildings.) My health slowly goes down, and if I look at the boxes I can tell I'm falling through the map. As far as I can tell, this isn't really a common problem. I've tried Compatibility Mode with Windows XP SP3, with the same results.
I am playing on Windows 7, using the non-Steam version.