Issue with the Connect Line Tool

[Corey]

Well, what a strange object I created indeed. With your clear tutorial, I have now fixed the object, but the issue still to some extent remains!

If I select all the 'Horizontal' vertices as shown in the attached image, and via the context menu click connect, the lines for some odd reason do nothing! Because I have already connected 'Vertical' vertices. I could manually select each edge, and click connect, then position the line to be approximately close to the points, but that would take ages, for the bottom. I have attached an image showing this too (On the Roof).

Image 1: https://www.dropbox.com/s/u4lwb3rk2q4vlhq/4.png?dl=0
Image 1: Part 2: https://www.dropbox.com/s/9quzhse0ux70mm6/5.png?dl=0
Image 2: https://www.dropbox.com/s/a846c2n5xhg5mcx/6.png?dl=0

And thanks for all your help so far, if this is my fault once again I apologize, otherwise fix soon please!