When I click "Test Connection" button, "Connection Failed" message is displayed

Please make sure that the following conditions are fulfilled:

MS SQL Server is installed on a machine which you're specifying in the EP.NET installer;
SQL server Username and a Password entered by you are valid, and the SQL user account has a permission to create a new database;
The SQL server is setup for using SQL (mixed mode) authentication:

If you are not sure if specific SQL user account has permissions to create a new database, try to use "sa" username.
To make sure that SQL account credentials are valid, check them by creating a test ODBC connection using "ODBC Sources" applet in the Control Panel.

Another way to check is to open the SQL Server Management Studio, and login to your SQL server using "sql authentication". If you can login using an sql user name, and password, then you are using the right info, but another problem maybe the name of your SQL server. Make a note of the server name you are logging in to, at the SQL Server Management Studio login, and make sure you use this name during the EP setup process.

Please note that for the case of using locally installed SQL 2008R2 Express with a default instance name you should enter (local)\sqlexpress in the EP.NET installer.