What your code is saying is that you want to connecto the database called 'rumpus.plus.net' on the local host. What you likely mean is that you want to connect to the host named 'rumpus.plus.net' and use some unspecified database. The DBD::mysql documentation describes the correct syntax to specify the host and database.
my $host = 'rumpus.plus.net';
my $database = 'somedatabase';
my $dbh = DBI->connect("dbi:mysql:database=$database;host=$host", $use
+rname, $password);