SQL queue doesn't start activation procedure SQL Server

The problem is likely to be that you didn't specify the CONTRACT when creating the Service, ie:

CREATE SERVICE [StoredProcedureService] ON QUEUE [dbo].[StoredProcedureQueue]([DEFAULT]);

Otherwise, the messages will be sent with DEFAULT contract, but your service doesn't support it.

You can probably see the error if you do:

select cast(message_body as xml),*
from StoredProcedureQueue

For me, it returns:

<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<Error xmlns="http://schemas.microsoft.com/SQL/ServiceBroker/Error">
  <Code>-8408</Code>
  <Description>Target service 'StoredProcedureService' does not support contract 'DEFAULT'.</Description>
</Error>

Another thing, among others, is that you shouldn't END CONVERSATION in your script: END CONVERSATION @dlg; but rather do it in the procedure.

Finally, you need to actually enable Activation by setting: STATUS = ON.

Script for queues + services:

drop SERVICE [StoredProcedureService] 
go
drop QUEUE [dbo].[StoredProcedureQueue]
go
CREATE QUEUE [dbo].[StoredProcedureQueue]
go
CREATE SERVICE [StoredProcedureService] ON QUEUE [dbo].[StoredProcedureQueue]([DEFAULT]);
go

ALTER QUEUE dbo.StoredProcedureQueue
    WITH ACTIVATION (
    STATUS = ON,
        PROCEDURE_NAME = dbo.ActivationProcedure,
        MAX_QUEUE_READERS = 1,EXECUTE AS OWNER
        )
GO

Logging code:

drop table tbl_Log 
create table tbl_Log (ID INT IDENTITY PRIMARY KEY, logtype nvarchar(100), logtext nvarchar(max), dateCreated datetime not null default getdate())

Procedure code:

CREATE PROCEDURE dbo.ActivationProcedure
AS
BEGIN
    INSERT INTO tbl_Log (LogType, LogText) values ('test', 'ActivationProcedure')
     DECLARE @conversation_handle UNIQUEIDENTIFIER;
  DECLARE @message_body XML;
  DECLARE @message_type_name sysname;
     WHILE (1=1)
  BEGIN
    BEGIN TRANSACTION;

    WAITFOR
    (
      RECEIVE TOP (1)
        @conversation_handle = conversation_handle,
        @message_body = CAST(message_body AS XML),
        @message_type_name = message_type_name
      FROM StoredProcedureQueue
    ), TIMEOUT 5000;

    IF (@@ROWCOUNT = 0)
    BEGIN
      ROLLBACK TRANSACTION;
      BREAK;
    END

    IF @message_type_name = N'DEFAULT'
    BEGIN
      -- If necessary handle the reply message here
      DECLARE @AccountNumber NVARCHAR(MAX) = @message_body.value('(Message/timestamp)[1]', 'nvarchar(max)');
    print @AccountNumber;
     -- Not needed if you have a service without reply
     SEND ON CONVERSATION @conversation_handle
        ('<ok>OK</ok>');
      -- Since this is all the work being done, end the conversation to send the EndDialog message
      END CONVERSATION @conversation_handle;
    END

    -- If end dialog message, end the dialog
    ELSE IF @message_type_name = N'http://schemas.microsoft.com/SQL/ServiceBroker/EndDialog'
    BEGIN
       END CONVERSATION @conversation_handle;
    END

    -- If error message, log and end conversation
    ELSE IF @message_type_name = N'http://schemas.microsoft.com/SQL/ServiceBroker/Error'
    BEGIN
       END CONVERSATION @conversation_handle;
    END

    COMMIT TRANSACTION;
  END
END

Test sending code:

DECLARE @message_body XML;
DECLARE @dlg UNIQUEIDENTIFIER;
-- Construct the XML message body
SET @message_body = '
    <Message>
        <barcode>PS23060094/9.9</barcode>
        <palletweight>993</palletweight>
        <timestamp>' + CONVERT(NVARCHAR(30), GETDATE(), 120) + '</timestamp>
        <processing_procedure>spProcessStep1</processing_procedure>
    </Message>
';

-- Begin a dialog conversation
BEGIN DIALOG CONVERSATION @dlg
    FROM SERVICE [StoredProcedureService]
    TO SERVICE 'StoredProcedureService'
    ON CONTRACT [DEFAULT] -- Important!
    WITH ENCRYPTION = OFF;
-- Send the XML message to the Service Broker queue using the conversation handle
SEND ON CONVERSATION @dlg (@message_body);