The alleged virus wasn't really an issue, as far as we can tell. It seems to be completely unrelated that the six-year-old modem just picked that particular moment to die. Once we got the new modem, it should have worked, but it didn't. Turns out that Cox had to fix some setting at the head office in Atlanta, but the first two tech support people I got just wanted to send someone out to our house, which wouldn't have helped.
I tweeted about it (while using the neighbor's wi-fi), and Cox's support team tweeted me back this morning. We also had a message on the answering machine this morning verifying that the problem was resolved, and sure enough, we were able to sign on. Yay!