This will work without trouble.
Set your TCP/IP settings to DHCP first, as most cable companies use this setting, unless you're paying for a static IP, in which case, use the settings they specify.
Now, some cable companies allow access based on the identifier of the network card. If you signed up for cable with another computer, and switch to this one, you may need to call tech support for the cable and tell them your new MAC address, which is the number that tells them the ethernet ID. You can find this number in Apple System Profiler under the network section.