OK, I'm not absolutely sure about the LK, but that looks right for the DPDT ON-ON-ON switches used in the 4004 basses.
DPDT = Double Pole Double Throw - 2 side by side switches that have 2 positions (and possibly a center)
ON-ON-ON = 3 positions, with center detent connecting both of the end positions.
So, as seen in the picture, when the toggle is down, the upper pins will connect to the center, so the single pickup wire will connect to the output. When the toggle is up, the bottom pins will connect to the center, so the two wires on the bottom left will be connected. In the center position, both top and bottom pins will connect to the center and you get all pickups connected.
So what's wrong? Well, about the only conclusions would be, the pickup is dead, the switch is bad, or the wire from the pickup to the switch is bad (this could also be a bad solder joint, the one on the top left doesn't look all that great, but it's hard to tell from a picture).
In reality, the whole thing is just a piece of junk and you should just ship it to me for proper disposal...
I have NO idea what to do with those skinny stringed things... I'm just a bass player...
) and the bridge pickup doesn't work, or should I say, with the toggle in the bridge position I get no signal. 
