When we try to install Umbraco, can get following error "Database connection initialisation failed."

This error shows that Sql server is not connecting. If you have right credentials then just add those in Web.Config of Umbraco.

 <add key="umbracoDbDSN" value="server=ServerName;database=UmbracoDB;user id=sa;password=YourPassword" />

Enter value of umbracoDbDSN

Now Database will install successfully.