You see, I have voicemail. And when you have new a voicemail message you can tell because instead of a solid dialtone you briefly get an interrupted dialtone (i.e. a beeping dialtone). However, this confused the dial-up modem on my laptop and kept returning with a "no dialtone" error message.
It also didn't help that I had muted the sound on the laptop, so it didn't occur to me originally that it might be the problem. I thought it was the phone cord or the port on the laptop itself that had gone bad.
What a shitty day.