Try changing the mac address of the ethernet card on the new mac to the same as it was on the old mac by doing the following:
To find the mac address on the old mac, go to apple -> control panel -> tcp/ip -> ethernet. Then go to "get info" from the file menu and write down the mac address.
Then on the new mac check which interface the ethernet card is - it will be en0, en1, en2 etc depending on whether you have an airport card, dial up modem etc. When you have identified this open terminal and type the following:
sudo ifconfig enX lladdr [new mac]
where X corresponds to the ethernet card, and [new mac] is the mac address from the old mac.
Then reboot everything and connect up the cable modem... hopefully this should get you sorted
