Well, this isn't going to be much help. But I asked wiser friends than I about these things, and here's the consensus. (And they might not be right). It can't be the modem itself if you have broadband and don't even have an analog phone line in the house. If the sound is coming from the computer's speaker (or speakers, how ever you have it set up) it could be some type of software - but how to locate the program running it is the mystery.
If you listen and it is not coming from the speaker(s), then it might be hardware - a physical noise - that just sounds like a phone ringing. The fan was suggested as a culprit. I think Lorie D. already suggested that.
But without knowing where the sound is coming from, what kind of ringing its making, and how loud it is, it's hard to come up with much more than that!