Boolean Difference won't work.

 From:  Michael Gibson
11599.3 In reply to 11599.1 
Hi Robert, you haven't done anything wrong. It can just be a difficult case for booleans to automatically determine separation when you place a cut that runs right along a lot of existing edges and geometry.

I've attached a file where I've split it into 2 using Edit > Separate and Construct > Planar.

- Michael