I tried to look up specifications on both those devices and they both
appear to be fairly old. Not that that really means much.

Ok. Log in to your modem. Does it have a DHCP server? If you have more
than one computer on your system Im betting it does. On newer ambit
modems you would look for Operation Configuration and see how many CPE's
are allowed and what the DHCP server is.

Some things you might try are, plug your ubuntu computer directly into
the modem and see if it gets a connection there. If not, I would suspect
your network card not being seen by the system, the network card not
working, or possibly the cable itself.

If you do get a IP, plug it next into the hub. I would suggest
unplugging everything else at this point. If it can get a ip there then
you have some questions to get answered. It might be that you are only
allowed so many computer to receive a IP address. If this is so then
you'll have to contact the cable company about dropping one of the mac
addresses that they have for your system.