From your reputation, I see you are new to Blender Stack Exchange. Although I've no official capacity to do so, let me welcome you to the community.
I downloaded and studied your original blend file, and found that the faces you originally obtained from the cylinder were not connected. By extruding these faces you would up extruding each of the cubes separately. Extracting the faces from the cylinder so that they were connected, or failing that, connecting the faces using the method Gandalf3 suggested, and then extruding would have eliminated the collision of the resulting cubes, although you would still have been left with interior faces. However, if you had switched to edge select mode, and selected the perimeter edges all around the set of faces, and extruded from that, you could have then used the Grid Fill tool to avoid the interior faces, too.