I'm having trouble opening the file, are you using a student edition?
Anyway, try moving the lines that are right on the edges of the part so that they hang off the part a little. A very tiny sliver can cause the zero thickness error. If you search that term on the forum, you'll find other cases where this happens, and how to avoid it.
I attempted what Matt suggested and it didn't help although I think I pinpointed the area it's going zero manifold. You could try moving the sketch line which defines the cut here. Not sure why you couldn't open it, Matt.
That's about as far as it would go before it gave an error.
As my friends mentioned you will get a zero thickness wall... You can cut it out from two steps.
Here is a video: