Enabling SQL Server Service Broker requires a database lock. Stop the SQL Server Agent and then execute the following:
USE master ;
GO
ALTER DATABASE [MyDatabase] SET ENABLE_BROKER ;
GO
Change [MyDatabase] with the name of your database in question and then start SQL Server Agent.
If you want to see all the databases that have Service Broker enabled or disabled, then query sys.databases, for instance:
SELECT
name, database_id, is_broker_enabled
FROM sys.databases