Recreating faux 3D objects

[pjanchon]

Hi,

I'm recreating an old design as part of logo. (Attached.) It is made up of 3 simple "3d" objects. The first object is a simple rectangle. I started by creating the rectangle, skewing it, then duplicating. I then used the create shape tool to create the "end cap". The problem is combing or joining these separate shapes results in the screen shot below - jagged edges that don't line up. Any advice or a better way to do this? The old graphic is a low quality jpeg so my goal is to create a new vector file suitable for all future uses.