How can I join meshes that are separated by dotted lines? I'm trying to create a book shelf, but after doing a series of loop cuts, some of my shelves are now doubled-up and I'd like to delete them.

As you can see in the image below, I tried deleting all of the faces and edges for one of the doubled up shelves in the hopes that the two parts would "snap together", but they are now separated by orange dotted lines. Is it possible to merge these two sections together now? I tried using the Merge tools, but none of them accomplished my goal.

How can I merge the separated edges with the mesh that I want to keep, and have the original shelf stay in place? If I am trying to do this in the entirely wrong way, Then i would appreciate being pointed in the right direction.
You can easily do this by first enabling Vertex Snapping

select the edges/vertices that you want to join.

Hold Control and move it along the Z.

Then, select all the vertices, you want to join, or simply press A to select them all. Press W and select remove doubles. This will join them so it is a connected mesh.