In addition to NetWallah's suggestions, the site may also be blocking according to the referrer URL, or by the user-agent of the "browser", or possibly even by a cookie (if the image URL is that of a CGI script). Try this code (which is completely untested):

#!perl -w

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

my $url = 'http://www.server.com/path/to/image.gif';
my ($referer) = $url =~ m!^(https?://[^/]+/)!;

my $ua = LWP::UserAgent->new(
    agent => 'Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 4.0)',
    cookie_jar => {}
);

# probably not needed, only needed if cookie is used
# to test for "real browser". highly unlikely, but you
# never know!
$ua->get($referer);

my $req = HTTP::Request->new( GET => $url );
$req->referer($referer);

print $ua->request($req)->content();
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