Hey,
   Thanks a bunch to everyone who commented, I greatly appreciate it.
   Just to make everything clear, the Control Panel I have now – I did not build this, but it came with the arcade when I bought it – has 2 Molex connections between the Control Panel and the arcade (You can sort of see this in the picture above).  Between these 2 connections, they handle both the power for the controls and their output.  Like Chris said, the Molex connections are tight, and really aren’t fast to plug and unplug.  The only reason I wanted to keep them was just so I didn’t have to re-make the existing plugs.  
   However, from what you all have said, it doesn’t seem like Molex is the ideal thing to use in my situation.  It seems like a lot more work and cost would go into Molex, than one of the other methods mentioned.  Also, I don’t really like the concept of using more than one encoder.  This seems expensive and wasteful, even if it is much quicker. It is way over my budget anyway.
    Thus, I am greatly leaning toward using the straight-through parallel port cable setup that Buddabing mentioned.  Even if it isn’t as speedy as cat5 cables would be, I would rather have all my controls in 1 or 2 connections, than in 4 or 5.  Plus it seems a bit cheaper to use just one or two cables.
    I have a question about the parallel port cable, though.  Do these straight-through parallel port cables have a separate wire for each pin? 
    If they do have a wire for each pin, this raises the question, are there different types of parallel cables?  I only ask because, I had at first wanted to use some parallel cables I already have, but after I played around with them, I found that running a current through one pin could be detected on a totally different pin on the other end of the cable.  I assumed this meant that some of the pins ran off the same wire.  Please correct me if I am wrong in this. 
   I have attached I picture of what I believe I need to do in order to use the Parallel cables.
   Thanks again.
Just as it is,
Flip Willie