On a default installation of SQL 2005 or 2008 Express the SQL Browser service is not started for security reasons. This makes it harder for TestCaddy running on another machine to connect.
To remedy this, either:

  1. The browser service needs to be started or
      To start the SQL Browser service: Click on Start, Run and enter "services.msc". Once the Services control starts, locate the "SQL Server Browser" and right click it and select Properties. Set the startup type to Automatic.
  2. The SQL instance needs to be configured to listen on a TCP/IP port.
      To configure your SQL instance to listen on a TCP/IP port: Open "SQL Server Configuration Manager", (shortcut is usually created in the start menu under Microsoft SQL Server folder) Open "SQL Server Network Configuration" and then "Protocols for InstanceName" (where instance name is the name of your SQL server). Double click "TCP/IP" and on the drop down menu next to enabled select "Yes", You will need to restart your SQL server for the changes to take effect.
      TestCaddy also needs to be given that port as part of the server details (in the Configuration Wizard, or if your TestCaddy is already connected to a server you can use File -> Database Manager -> Change), which is done by appending a comma followed by the port number to the server name without the instance name, e.g. if the port number is 1433 (this is the default port) and full SQL instance name is\SQLExpress then for the Server field enter,,1433

The following Microsoft KB discusses this for SQL 2005,
but there doesn't seem to be a similar official article for 2008. The following article may be some help,

If you ask TestCaddy to install SQL Express 2008 for you it will try to start the SQL Browser service. If it can then it will set the SQL Server connection details to use the IP Address of the machine. If it can not, then it will use 'localhost' and present the warning that begins, "Could not start SQL Browser Service" which directs to this FAQ.
The SQL Browser service may fail to start if there is more than one instance of SQL on the box, e.g. side-by-side SQL 2005 and 2008 installs. In any case the issue should be able to be resolved. Contact TestCaddy technical support if you'd like help with your particular situation. Also Note: Your firewall might also prevent remote connections. Sqlserver.exe and sqlbrowser.exe need to be added to firewall exceptions in order for SQL 2008 Express to accept remote connections. Refer http://blogs.msdn.com/sql_protocols/archive/2006/09/30/SQL-Server-2005-Remote-Connectivity-Issue-TroubleShooting.aspx