5100 modem working for 2 years then problems

I have an Inspiron 5100 w/Win XP, about 2 yrs old. The modem is a Conexant D480 MDC V.92. Attachment to the internet is via the dial-up phone network and has always, until now, worked fine. I use the notebook some at home but mainly at remote sites. My home phone is rotary pulse and the remotes are all touch tone. A couple of months ago I found, at a remote site, that after signing off of the Internet the modem did not hang up the phone line. I then found that it was sometimes taking several tries to sign on to my ISP at home and I had to disconnect the phone line from the computer between each try, to hang up. I now cannot sign on at all at home. I just tried with the computer volume turned completely up and was barely able to hear the rotary pulses, I heard an answer, some tones then a voice saying "if you'd like to make a call please hang up and try again". Even since I have stopped being able to sign on at home, I was still able to the last time I was at a remote site. The tone dialing must be stronger. The modem properties device status, of course, says the device is working properly.

I am assuming that the modem is bad, but would sure like some confirmation from someone with more experience in this area. I've been using computers for years but have never had a modem problem! Can I get some opinions out there?