How To resolve “Database Mail is stopped” error

Source

You try to send Test mail from Database mail but it throws below message-
Msg 14641, Sev 16, State 1, Line 81 : Mail not queued. Database Mail is stopped. Use sysmail_start_sp to start Database Mail. [SQLSTATE 42000]
1. To investigate this issue, firstly confirm whether Database Mail is enabled or not by executing below queries in SQL Server Management Studio-

       sp_configure 'show advanced', 1; 
       GO
       RECONFIGURE;
       GO
       sp_configure;
       GO

If the resultset show run_value as 1 then Database Mail is enabled.
2. If the Database Mail option is disabled then run the below queries to enable it-

       sp_configure 'Database Mail XPs', 1; 
       GO
       RECONFIGURE;
       GO

       sp_configure 'show advanced', 0; 
       GO
       RECONFIGURE;
       GO

3. Once the Database Mail is enabled then start it using below query on msdb database-

       USE msdb ;       
       EXEC msdb.dbo.sysmail_start_sp;

4. To confirm that Database Mail External Program is started, run the below query-

       EXEC msdb.dbo.sysmail_help_status_sp;

5. If the Database Mail external program is started then check the status of mail queue using below statement-

       EXEC msdb.dbo.sysmail_help_queue_sp @queue_type = 'mail';

For more details please check the link http://technet.microsoft.com/en-us/library/ms187540.aspx