PROBLEM: I need to know if a database has Service Broker enabled.

SOLUTION: The query I have listed below will provide you with the information you are looking for and if a database master key has been created for a database.

SELECT name [DatabaseName]
     , is_broker_enabled [IsServiceBrokerEnabled]
     , is_master_key_encrypted_by_server [HasDatabaseMasterKey]
  FROM sys.databases
 WHERE is_broker_enabled = 1