Just because people are connecting to a db does not mean that the db instance is where you think it is. If people are connecting to a database that you are trying to maintain/troubleshoot through an application you need to find where the connection string in the application is. It should tell you the instance name where the database is located.

It is also possible that SQL Server is installed on the server you are trying to access yet you are just not seeing the services in SQL Server Configuration Manager. For example in your screenshot you are running SQL Server Configuration Manager that is from SQL Server 2008/2008 R2. If a newer instance of SQL Server is installed, like SQL Server 2012 it will not be able to see those newer services. Go to Control Panel > Services and see if any SQL Server services are listed.