Have you set permissions on the folder? I believe they'll need to be 0755 or 0766, Global Read/Write, in order for your directory to be accessible. If the folder is below the webroot, as you've described - so that it's available to the public (and you can get a file by going to http://example.com/files/private/foo.bar) then your method is correct.

Remember the web root is different from the server root, and I'm not 100% sure that the File Downloads module can accept a relative path. You may need to use a full path. (Shawn please, correct me if I'm wrong here..)

It's not a database problem, though. It is most likely a permissions problem, or a PHP/Apache issue (the open_basedir problem I mentioned before).