Whenever you move a cable connection from one PC to another, it's best to cycle power on the cable modem. What's happening is that the cable company has given the laptop a "lease" for an IP address that is attached to the MAC address of the laptop's Ethernet adapter. If it doesn't find that MAC address, it's not going to provide an IP for it.
The MAC address is a hardware address.
Try rebooting your cable modem after connecting to the PC.