You'll more than likely need a router. Most cable modems do not have 'routing' built into them like DSL gateways do (which are basically DSL modems and a router together in one box). Depending on your needs, they can run from $20 for cheapies up to over $100 for higher end gaming wireless routers. You'll be able to find a router (either wireless or wired) at any Walmart etc.
Basically, you need the Router to assign that 2nd computer an IP address. The current one you are getting is assigned by the cable modem (which can only assign one)