In my company we use SQL Server Broker when trying to enable in the staging server it was taking a long time to enable it. This is very crucial because when you want to enable this on your live server you can't afford to have a down time.
The below was taking long time but I got the query wrong.
ALTER DATABASE [<dbname>] SET ENABLE_BROKER
Try the query below:
alter database [<dbname>] set enable_broker with rollback immediate;
If you want to check which of your Databases are SQL Server Broker enabled:
SELECT name, is_broker_enabled FROM sys.databases