Well, I was trying to do the same thing. Had lots of trouble. Couldn't figure out why until I realized that the file I was trying to initialize wasn't being loaded.
my $ua = LWP::UserAgent->new;
$ua->cookie_jar(HTTP::Cookies::Netscape->new('file' => '<your cookie f
+ile here>' ));
my $url = URI->new( '<your URL here>' );
my $response = $ua->request(HTTP::Request->new(GET => $url));
but the above code works. If you follow other examples, you'll end up creating a seperate "cookie jar" and attaching it to your user agent. Just make sure your cookie file is being read because nothing really lets you know it didn't work (I'm sure there is a status or something, but I didn't get into the details and it didn't die or anything on its own).