If I recall correctly the SQL Engine service of SQL 2000 is named "MS SQL Server". When you have the services sorted on name (default) the Engine service is -not- listed next to the Agent service.

How does your WinTel group wants to create their backups? Are there additional related error messages in the SQL log or in the Windows Eventlog?

Because the datafiles are locked when a database is online, you need to have a backup application that handles these situation. It's better to create backups of the databases by using a SQL backup (native or third party).