This sounds like the micro-relay on the modem board has gone bad. This relay acts like the phone going off hook to connect. If the relay stays operated it will keep the line seized. Time for a new modem?
Good luck,
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After logging of and disconnecting, the modem continues to keep the phone line. It used to work fine and then all the sudden it wouldn't disconnect. It says it is and it sounds like it does, but my line is still busy and I cannot use my phone unless I unplug the modem line from the wall and plug in the phone. I have had SBC out to check thye line - it is fine.

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