Thanks for the clue. After some more research along that line I fixed by changing my GET code to look like this:

$ENV{'PERL_LWP_SSL_VERIFY_HOSTNAME'} = 0;

my $ua = LWP::UserAgent->new( ssl_opts => { verify_hostname => 0,
                                            SSL_verify_mode => IO::Soc
+ket::SSL::SSL_VERIFY_NONE,
   },);

my $req = HTTP::Request->new( GET => 'https://xkcd.com/');
my $response = $ua->request($req);
my $content = $response->content;
my $sitePrefix = 'https://xkcd.com/';
[download]

Now it works again. Thanks everyone!