Why not:

use IO::Socket;   # distributed with Perl

my $web = new IO::Socket::INET("www.example.com:80")
  or die "Couldn't connect: $@";
print $web "GET /some/file HTTP/1.0\n";
print $web "Host: www.example.com\n\n";

$/='';
my $results = <$web>;
[download]

Now just parse out the headers, look for errors, etc. This will not follow redirects (e.g. "/some/directory" -> "/some/directory/"), and is generally only usable for the most basic case of web requests. If you want any real abilities outside of this, you'd be far better off using LWP, or at least reading through it and pulling out the code that you need.