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They can be using the Mac address of your ethernet/wireless Card.
If you have a cable modem and live in a Time warner area unplugging it for a few hours and then rebooting might change your Ip
Unplug the modem they gave you for 72+ hours, that is your only chance of getting a new IP.
David, the MAC address is not used for security outside of the L2 domain. An internet host/site cannot filter based on MAC address. The MAC address of all packets destined for a host shows up as the MAC of the nearest upstream L3 device, so filtering by MAC is not useful for anything but the ISP who manages the connection.