This is what I would try:
(1) Be sure the db_owner for the SQL Server database has access to the network location you are trying to write the backup to (I assume you are backing up the database on the same server as the SQL Server instance being ran)
(2) Add WITH EXECUTE AS OWNER after the CREATE PROCEDURE command as such (the WITH EXECUTE AS... command will be required in SQL Server 2014, FYI):
CREATE PROCEDURE [dbo].[NWPS_CREATE_DBBACKUP]
(
@p_OriginalDBName varchar(1000),
@p_DestinationSQLServer varchar(1000),
@p_DestinationBackUpLocation varchar(1000),
@p_DBBackUPFILENAME nvarchar(1000) ,
@p_error_code int OUTPUT,
@p_error_msg varchar(1000) OUTPUT
)
WITH EXECUTE AS OWNER
AS
Doing this will allow the procedure to execute as if the db_owner was running the procedure regardless of what account is calling the procedure as long as the calling account has EXECUTE permission.