...more info:
I'm not sure, but I think the problem is at the OS level. When I connect the Cat 5 cable, both the modem's and the Linksys Ether net card's status lights turn on, just like as if connecting to a router. I know the Ether card works, because six months ago (when I was living some place else) I connect to the Internet via this Ethernet card to a router.
The strange thing is that when I go into the Properties of this NIC card, and click on Internet Protocol (TCP/IP), ...Oh God, I just fixed it!
For some reason, the Internet Protocal (TCP/IP) check box was unchecked...go figure. I checked it and everything started working immediately! FknA! (excuse my French.) Why it was unchecked in the first place, I don't know. Anyway, I'm getting some impressive bandwidth now.
And all because I asked for help.