I have seen this happen to other modems after they were damaged by a lightening strike.
None the less, it sounds as if you are getting a dialtone, but the modem never receives a carrier from the distant end (I am assuming that you receive a NO CARRIER).
Open Hyperterminal and use the modem to dial your ISP. Make sure to set AT L3 so that you can hear the call progress tones yourself.
Just use AT DT <phone number>. If you hear carrier from the distant end, but the modem still returns a NO CARRIER response, then your modem is probably broken.
You can try issuing an AT &F to reset to factory defaults, but your modem may well need to be replaced.
Modems are VERY cheap now. It is probably quicker and easier to simply replace it.