The following database error occurred: [Microsoft SQL Server Native Client 11.0] : Named Pipes Provider: Could not open a connection to SQL Server 
Environment: SAP BI Platform 4.1 SP6 P4
I have got this error while refreshing a Web Intelligence report. After reading blogs I even tried to ping the Database server from the Application Server where I installed the SAP BusinessObjects. I get results. 😕
But the issue here was with port 1433.
Port 1433 from Application Server to Database Server was closed. With help of Firewall Admin team this was opened and everything works fine after that.
Hope this helps!