Well Whatever the above solutions are, they are correct.
But I would like to give you one more solution may work for you.
If you are using windows XP then just visit the windows Update website and then go to the hardware link there on the left and then allow it to search for any hardware update. By default if you are using a Dial-up modem from COXINNAT then there will be an update for it called PCI MODEM, download it and install (Windows XP will download and install automatically if you allow it to download)
Once it is installed you will have to restart your PC, Now your STEREO SPEAKERS (from the one which gives music) will be treated as the modem speaker while you are dialing.
Which means that now during dialing your PC Speakers will make the noise, since you do not want the noise, just turn the knob of the Speakers to OFF position and u are done ,or you can also turn it to the minimum level.
Try it out.