Can't see it being a problem with the modem. They usual either work or dont; if its dialled up and made the connection then its done its job, and is likely working. As already requested, had this happened before ever trying to connect to internet?
Internal or external modem? If internal, did you recently fit it? If so try to seat it as far apart from the sound card as possible. Conflicts arising from a sound card next to a modem are common.
I would be more inclined to look at the ISP, the phone connection, connection properties, etc. before a broken modem...