Modem: Cisco 2100
Besides the usual resets and power cycles, and I have done all of the various configuration chants and incantations with firewall rules and udhcpc.
DD-WRT does not seem to have this problem. When the router starts up with that firmware, it seems to get a very short lease with a 192.x IP. It expires seconds later, at which point the router grabs a new, public IP from the modem.