When I was on cable, I always used to notice something a bit quirky.
If I have a router with mac address A connected to the cable modem and I power on the cable modem, and then the router, the router would normally DHCP shout and have no problems being allocated an IP.
If I then disconnect that router, and connect another completely different router, with mac address B, and let it try and DHCP, it would fail (it just wouldn't get any responses from its DHCP shouts). Only if I turn the cable modem off and back on would router B then be given a new IP via DHCP (the network responds as normal to the shouts). The IP is usually completely different, as this is a new mac address the network hasn't seen before.
I've seen this behaviour time and time again on cable, and it really puzzles me. I don't really understand what's going on but it certainly ain't normal, and it seems to me to be some weird side affect of the whole cable infrastructure that causes this. Maybe you can explain? Might be indirectly upsetting the Cisco, but this is purely speculation.