Its fun how the code appears to work (returns the HTML output), against my local testserver, but not on the server I have the issues with.
This is the code, correct me please if I did any lazy things that can make it work :-P

use LWP::UserAgent;
use HTTP::Request::Common;

{
   package MyUA;
   use vars qw(@ISA);
   @ISA = qw(LWP::UserAgent);

   my @try = (['username', 'password']);

   sub get_basic_credentials {
    my($self,$realm, $uri, $proxy) = @_;
    print "$realm:$uri:$proxy => ";
    my $p = shift @try;
    print join("/", @$p), "\n";
    return @$p;
   }

}

my $ua = MyUA->new(keep_alive => 0);

my $req = HTTP::Request->new(GET => "http://mail.isnitro.com:49282/nav
+igation/nav_home.shtml");
my $res = $ua->request($req)->as_string;
print "Res: ", $res;
[download]

The Digest realm is as far as I can see, static against "GWAVA Console".