What would be more helpful than "Konnte Datenbankverbindung nicht herstellen: $!" (which, according to babelfish means "Data base connection could not manufacture") would be to use DBI's $DBI::errstr, which will give you the exact connection problem.

my $dbh = DBI->connect("dbi:mysql:$database:$db_server", 
"$db_user", "$db_pass") or die "Error: $DBI::errstr $!\n";
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I really, really hope that you didn't enter the real login info in your post. But if that was the real info (change it!), the $DBI::errstr was "Unknown MySQL Server Host (db07.puretec.de)".

Jasmine