I received this error following a SQL Instance upgrade from MSDE to SQL Server 2008 R2 Express and tried to connect to the SQL Instance remotely via a third party application.
[DBNETLIB][ConnectionOpen (Connect()).]SQL Server does not exist or access denied
Fortunately the solution was simple:
Start the SQL Server Browser service and if required change the Startup Type from Disabled to Automatic
I looked up why the SQL Server Browser service is now disabled by default and the reason is simply that it’s a security best practice to disable the service.