If your modem has an unending handshake or stops with an error message BEFORE the "Verifying username and password" appears, there is a problem with the modems negotiating the connection.
Be sure that the correct modem is selected for the connection in the Dial-up Networking folder.

Check to see that there are no unnecessary extra settings in the Modem properties.

Check the dialing properties of your connection and be sure the modem is using the correct (and newest) driver.

If you have been having any static problems with the line, this problem may occur. To minimize interference, remove devices that are sharing the line, including splitters, digital cable, fax machines. Try disabling the v.90 or v.92 protocols or try resetting the modem using AT&F or AT&F1

Try connecting using Hyper Terminal.
If you can connect through HyperTerminal, then the modem is probably not the problem. The problem may instead be with Dial-Up Networking. Try uninstalling/reinstalling Dial-up Networking. If you have Windows XP and have pulse dialing and the dialing properties are set correctly for pulse, try adding a "P" before the phone number.
If you can't connect through HyperTerminal, the problem is most likely the modem or the phone line. Make sure you are using the correct (and newest) modem driver.

If you have changed your phone service recently or if construction is being done on the lines in the area, problems may also occur.
If your modem handshakes 2 or more times, this indicates that there is either noise on the line or that the lines are not capable of a v.90 connection. Try disabling the v.90 or v.92 protocols.