The plastic connectors on telephone cables and splitters should be in good condition, and make a solid connection into corresponding jacks. Surge suppressers which provide modem line protection should show positive indicators for power and active surge protection.
Most external modems have an additional jack for connection to a telephone.
Make sure the line is inserted into the jack that does not have an icon for a telephone associated with it. Check the connection of the modem with the computer. If the modem is not connected, or loosely connected with the computer, do not push the connector in. The safe method to reconnect is to power the computer down, and re-seat the connector. Some external modems need their own power source and some are powered directly through the computer.