Backup & Migrate not working because of perrmission settings? what should they be?
Well last time I had the same problem what I did is connect with fillezilla and right-click to the root folder of my site then change permissions to 777 filezilla will go through all your folders and sites and will change all the permissions automatically, it will take some minutes but then all your folders and files will have 777 permissions, try again to use your back-up and migrate, do not forget to clear chaches, after use backup and migrate change the permissions to your settings.php and your private folder in sites/default/private that forlder is where backpup and migrate saves the backups.

Also make sure the the database user you are using with your drupal has all the privileges.