I’ll think out loud here for a minute...
First off, the “ringing” sound that other people hear when they call you isn’t the same thing as the “ringing” sound you hear.
The first one — “Ring Tone” — is a noise generated by your exchange. All that tells you is that your exchange believes that your line is not engaged.
The second one — “Ring Voltage” happens between your exchange and your phone/modem. It used to be +12volts, and it used to physically make bells ring on your phone. With digital phones and networks it may not be that voltage anymore.
So they are entirely separate things.
The next complication is that PABx systems — particularly the older ones — can be set up with something called “ring/noanswer”. This means that if all lines coming into your PABx system are engaged, and another call comes thru, it will ring rather than give a busy signal...
So, a couple questions to start out with:
1) Are you on a PABx?
2) What happens when you plug a normal handset into your wall jack and one of your friends calls you? Does it ring?
The first question will help us isolate “ring-noanswer”, and the second question will help us determine whether you are receiving “Ring Voltage” — your telephone and your modem need to receive this in order to ring.
Stepping out now for a little while...