I know this will sometimes work for DSL, not sure about Cable, but here you go:

You'll need to disconnect the coax coming in from outside from your modem, and leave off for 15-30 mins, to give the ISP's server time to clear your MAC address from it. After that, reconnect and renew.

I'm behind a router/firewall, so I can switch from DHCP to a static IP in the same range and be ok, but I'm usually too lazy and just wait it out.