When the modem is not dialing or responding, it may be anything from something simple or more serious such as hardware issues.

Check the information on these pages for information and steps that may resolve the problem.

Additional Reference from Microsoft:
Q191444: Err Msg: The Modem Is Not Installed or Configured for...
Q124075: TAPI Apps Can't Dial Unless UniModem Is First Listed Provider
Q158114: Err Msg: Error Messages Occur When You Attempt to Use Modem

In addition to referencing the links above for troubleshooting steps, please note the following:

Power Cycle:
Whether or not you are receiving a specific error, it is recommended that the first step you take is to power cycle the computer and modem.

Check line and remove devices:
See if the phone is off hook or if another device is on the line and possibly using the line - this includes handsets, spike blocks, splitters, another computer, fax or answering machine, call zapper, etc. Remove all other devices from line and note that even those on a second phone line as there may be a problem with internal wiring.

Check that modem is plugged in correctly:
Make sure that the modem cable is plugged into "Telco" or "Line In/Line" vs. "Phone" on the back of your computer and remove ALL devices, splitters, surge protectors between the modem and wall jack. Be sure the modem cable is seated firmly in the jacks on both ends of the cable.

Correct modem selected in connection:
Check your Dial-up Networking connection and be sure the correct modem is selected for the connection.

Voice Mail messages:
If you use voice mail and here a stuttering when the modem tries to dial, you likely have messages waiting. Clear the messages and try again.

Modem driver corrupt, modem damaged or incorrect initialization string:
It's possible that a modem initialization string that was entered is incorrect for your modem. Check your modem settings for a modem string. If an initialization string is in the extra settings field, clear it out, reboot and attempt to dial again. In addition to an incorrect modem string, your modem driver may have become corrupted. Locate your modem driver and reinstall the modem.

The modem may fail to respond if it was damaged from a power strike through the phone line during a storm.

Check your settings:
Check your dial properties including the location (area code for local dialing).

Determine if Windows can communicate with the modem:
Determine if Windows can communicate with the modem by querying the modem through the Diagnostics tab of the Modem Control Panel or sending ATi commands to the modem using Hyperterminal.

If there are AT command responses, the problem is usually with the cables or specific program/component being used, not with modem or modem driver. If there are no AT command responses and you are unable to remove or reinstall (autodetect) modem successfully, there is most likely a resource conflict. Check the Windows Device Manager by going to Start > Settings > Control Panel and selecting "System" and finding your modem. If there is a resource conflict, contact your computer manufacturer or take your computer to a repair shop.

This step is particularly relevant if you recently added a new modem or other hardware. Also be aware that when replacing a modem, a "ghost" modem may remain. The removal of a ghost modem requires complete removal of the modem, com ports and modem .inf files and disabling external serial ports in the CMOS setup. Take your computer to a computer repair shop to have this done if you are not comfortable with this type of task.