Well, it may work, but would probably be a pain to configure.
Also, parallel is incredibly slow compared to ethernet. You would be just as well off putting dialup on the other computer.
Is one of your computers running WinME or Win2K?
If it is, then you have something called internet connection sharing, if not then you will have to find 3rd party software to do that. Either way, you will avoid having to buy a router (which can be expensive, in the neighborhood of $200)
Buy extra network cards ($15 each), and install them so that you have 2 network cards in one computer, and one card in the other.
The computer which has 2 cards will act as the gateway. Configure one fo the cards in the gateway machine to work with the cable modem using whatever settings they tell you to. Plug the cable modem into that card.
Use internet connection sharing (either the program or microsoft wizard) on the gateway computer to share the internet connection to the internet on the first network card with computers connected to the second network card. Let Windows do it's magic.
Buy a cheap hub (maybe $30 - switches are better, but cost more)
Plug the uplink of the hub into the second network card on the gateway. Plug all the other computers into the hub. Set all their tcp/ip properties to "Obtain an IP automatically" and you are good to go. Much faster than parallel, and relatively easy to set up (though not as cheap as parallel, but cheaper than router)
