Sounds like you've got the modem and/or router configured in such a way that modem's configuration "wishes" are being passed through to your LAN.
You should be able to change that behaviour by reconfiguring the two devices; give us the exact make/model of both the modem and the router so that we have some specifics to work with.
Also- have you installed connection-related software from your ISP on the individual computers, or does the ICS/shared gateway configuration just seem to be automagically forced upon the systems by the modem?
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Wombat At Large
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