The larger box indicates a group or component. Try exploding it to start.
Hard to tell without the model, but a couple of questions:
-Are your individual 2d elements groups or components? If so, they will attach differently.
-Are the objects displaced in space, or do they actually touch?
Try selecting an element, hit ‘M’ for Move, and grab the corner. Take it to the corner of its mate, so you are aligning points that are supposed to touch. Is there a snap when they attach? That’s the joining.