Try out DA 1.20.5 (which I'll force out in a day or so).. it's already released, but it uses a higher privilege for the mysql dump, so the password issue will vanish. (database restore still requires correct passwords)
That's what it does to a temp location before sending the file to you. Also checkout the /var/log/directadmin/error.log for any possible clues. Or to state the obvious, login to phpmyadmin and double check the there is data in the database
If the file is still empty, how large is the gz file once it's downloaded? When I extract it manually, it create a tar file, but the "tar" file is actually the raw sql file, and there is no tarball at all. Just a quirk in the way my uncompressor program works in windows.