Sounds like the "white box" is an ethernet hub.
So, in order to share your connection, you'll need to plug it into a "router" that will handle directing the traffic among all the different computers connected on the network. A simple 60$ stand alone router is probably your best bet. There are other methods (internet connection sharing in XP), but they are less flexible and probably more work.
Run the modem into the router, then plug the router in to the hub. That should be enough to get you all connected (taking some guesses at how your place is setup).
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