Are you powering the modem down for about 15 seconds or so when switching from the desktop to the laptop?
Your cable modem might have an ARP table that is storing the MAC address of your PC's NIC and not allowing another entry for the laptop's NIC, thus you will not get an IP address from your ISP's DHCP server.
Your cable modem might have an ARP table that is storing the MAC address of your PC's NIC and not allowing another entry for the laptop's NIC, thus you will not get an IP address from your ISP's DHCP server.