Internet Explorer Ver.5* : Why does the [A connection with the server could not be established.] error message appear?

Why does the [Internet Explorer cannot open the Internet site https://[address]. A connection with the server could not be established.] error message appear and the webpage cannot be displayed if there is something wrong with the setting of Internet Explorer Ver.5*?

The procedure below explains 2 kinds of environment:
A. Access to the Internet with dial up connection.
B. Access to the Internet via proxy server with network connection.

[Procedure]
1. Click [Start] -> [Settings] -> [Control Panel].
2. Double-click the [Internet Options] icon.
3. Click the [Connection] tab.

-- A. Access to the Internet with dial up connection.--
1. Select [Always dial my default connection] in [Dial-up settings].
2. Confirm that the [Perform system security check before dialing] box is checked.
3. Select a connection name you want to use in the box that displays dial up connection name.
4. Click the [Settings] button.
5. Establish each of the settings as follow:
- Confirm that the checks in both the [Automatically detect settings] and [Use automatic configuration script] boxes in the [Automatic configuration] section are removed.
- Check the [Use a proxy server] box and enter the settings in [Address] and [Port] only when they are provided by your Internet Service Provider (ISP). Contact your ISP for the detailed settings of the proxy server.
- Type [User name] and [Password] provided by your ISP in the [Dial-up settings].
- Confirm that the check in the [Do not allow Internet programs to use this connection] box is removed. (This is not applicable to Ver.5.5*)
6. Click [OK] to close the dialog box when you complete the settings.

If you have several dial up connections, there is one connection that attached [(default)] at the end. That connection is currently set to use for connecting to Internet.
If you want to use another dial up connection to access to Internet, click the connection name and press the [Set Default] button.

B. Access to the Internet via proxy server with network connection.
1. Select [Never dial a connection] in [Dial-up settings].
2. Make sure that the [Perform system security check before dialing] box is checked.
3. Click [LAN Settings] in [Local Network (LAN) settings].
4. Establish each of the settings as follow:
- Confirm that the checks in both the [Automatically detect settings] and [Use automatic configuration script] boxes in the [Automatic configuration] section are removed.
- Check the [Use a proxy server] box and enter the settings in [Address] and [Port].
- Check the [Bypass proxy server for local addresses] box when accessing to the web server in the network (Intra Net) is not via proxy server.
You can set the address that does not access via proxy server in [Exceptions] in the [Proxy Settings] dialog box by clicking the [Advanced] button.
5. Click [OK] to close the dialog box when you complete the settings.