I here it open up when the phone number shows up like a little blup sound. I
think this is what your talking about. Is that relay part of the moden or?
Would the modem need replaced in this case or the relay can be fixed cost
effectively. There just no dial tone after that.
More often, that relay fails because a PNP driver transistor fails.
Transistor either fails shorted (modem does not hang up phone line) or
fails open (modem does not connect to phone line). If you hear a
relay clicking, then other parts in modem's DAA side may be damaged
such as lower resistance resistors.
Tracing the DAA circuit is easy. Follow PC traces from phone line
connector through small and conductive devices and via one transformer
to that relay. Each side of the relay 'switch' should connect each of
two center contacts on telephone jack.
Cost of damaged materials is trivial. However finding those cheap
devices (transistor, resistor, etc) can be expensive and challenging.
Also challenging is soldering a part that small. Cheaper is to buy a
new modem. However I have a few modems that were repaired and work
just fine a half decade later.
Diagnostics will report that motherboard computer can talk to modem
computer. But modem computer does not know if relay has failed as
noted by Elmo. Modem computer can only order that relay closed,
listen for a dialtone, hear nothing, and complain. If that relay does
not close or if some connecting part to phone line has been damaged,
then modem computer will only see 'no dialtone detected'.
Finally, why was that modem damaged? If damaged by a surge, then
most likely reason in N America is a surge that entered on AC mains.
Surges seek earth ground. Phone line should already have a well
earthed protector (which you should inspect). Therefore the surge
that seeks earth ground enters on AC electric, passes through
motherboard and modem, then obtains earth via phone line. Incoming on
AC electric. Outgoing to earth ground via phone line. After passing
through everything, then something in that surge path fails. Often
damaged is the PNP transistors that drives an off hook relay, or other
parts on modem's DAA (phone line) side.
Whereas the phone line has an earthed 'whole house' protector, AC
electric probably would not and does require a properly earthed 'whole
house' protector. AC electric is the most common source of electronic
destructive surges.