I've used the "Join" command for this in the past.
Notice that all of your parts are shown as surface bodies. That indicates that you picked the "Geometry to save" as "Exterior faces". If you had picked "Exterior components" or "All components" you would have gotten solid bodies. You could then use the "Combine" command to join the bodies into a single body. Note that the bodies must all have coincident faces to get a single body out. You might have to extend some faces (try the Move Faces command with the Offset option) to get them to join.