said by mh754:
To cork's question -- I had the computer directly connected to the cable modem, to establish that the modem was online and internet access was working. Then I unplugged the Ethernet cable from the computer (disconnecting it), and moved it to the blue Ethernet port on the Vonage box. For some reason, the Vonage box couldn't complete the initial handshake to get connected.
Anyhow, problem solved -- thanks for the helpful advice!
Just about any time you physically disconnect one piece of Ethernet equipment and "replace" it with another you'll have to let whatever's doing the routing (in this case, the modem) learn about the new hardware before it can be used. The reboots were necessary to reset all of the MAC and IP addresses and buffers.