What did you do to alter the settings on the Dial Up Connection?
I recently had a case where I had 2 dial up connections from one box and while the one straight to the bank worked perfectly the one to the Health Insurance Commission refused to dial out. The problem was finally found to be in the setup of the modem dial up connection to the HIC and I only picked this up by removing the connection and setting it up from scratch till it stopped working. If the Dial Tone is disappearing the moment that you plug in the phone line to the modem it sounds as if the computer is grabbing the line and not releasing it so instead of looking at a faulty modem I would delete the dial up connection and start again.
If the modem is faulty on an ATX Power supply with the computer turned off the Dial Tone should still be missing is this the case? If not then I would be looking at the setup of the modem. There are many changes that you can make to the way that a modem works and one wrong one can cripple the connection. In the case mentioned above the Tech Support person insisted that it was a faulty modem but when I sat on another phone line and dialled into the bank it made her sit back and think that just maybe there was something in their setup that was at fault.
It was a wild idea to her as that was the way that they always setup the modems but in this particular case it broke the connection and the Dial Tone disappeared on this one to but in this case only when that Dial up connection was activated and before it dialled out.
Start with a Basic Setting for the modem and make one change at a time until it stops working. This will have to be an entire Manual Setup so ignore any Setup Programs and do it all Manually.
Col