|It sounds like you just need to clear the ARP table of that Time Warner cable modem. |
Some cable modems (DSL too) can bind to the MAC addresses to the devices behind them and have to be "released" to put a new device behind it.
What Curt R. said is true, the modem is probably "registered" (bound) to that Linksys modem and will not connect to any other device. You can clone the MAC, but sometimes that does not work.
To properly clear the ARP table of the cable modem :
Disconnect the coax cable.
Disconnect any ethernet cable running to any router behind the modem, and disconnect the power to that router.
Wait at least 1 minute.
Start from the wall and reconnect all of the connections. Waiting for each device to fully come up before moving to the next.
When you just disconnect the power to the cable modem and let it sit, there is still current coming through the coax, and it will not clear the ARP table. Letting the modem sit in a complete off state basically sets it back to default, factory settings and you can put whatever you want behind the modem.
If this does not work, then you would have to call Time Warner and have them remotely clear any binding that the modem is doing.
Hope this works.