I'm not sure what is going on here. But let me hazard a guess.
Many users leave on their computers 24 hours a day. They successfully use their dialup modem then end their connection or are interrupted by connection loss. They later start a new dialup connection but receive an error message that the modem is busy, port is open or something similar.
Some dialup computer applications occasionally fail to reset the modem after a telephone line connection loss. The result is that none of the telephones extensions on that line can find a dial tone so no one can use the telephone.
You can reset the modem by turning off power to the card. Turning off the computer doesn't always work because some computers (ATX power supply) provide standby power to network and modem cards through the system mother board. External modems (connected to a serial port) have their own power switch that can be cycled on and off to reset the unit.
The brute force solution is to disconnect the power plug to the power supply (usually located at the computer case rear) or use the sometimes present power switch also located on the power supply located near the power plug.
Assuming you use Microsoft Windows, bring up hyperterminal from Start/Programs/Accessories/HyperTerminal and start a connected session. Type the terminal command ATH and most modems shall reset into standby mode.
On some occasions, the modem might be damaged as one of mine are. The modem component that hangs up has failed and the only way to return the dial tone is by physically disconnecting the telephone cord.
Tom Glenchur, December 2004