If you have the cable modem connected to a simple switch or hub and then all the computers hooked up to that hub, then the computers will be competing for an IP address since most internet providers lease you only one address. You need to have the modem hooked up to a broadband router, the broadband router set up to offer DHCP, and then the computers hooked up to the router.
If the router's DHCP is turned off or the router is set up as a simple access point, it may allow DHCP requests out to the cable modem and then you'll have all sorts of trouble.