HTML::SimpleLinkExtor only gives you a list of the links in the webpage. To check if you can connect with the resource pointed to by the link I used the head function from LWP::Simple. In scalar context it returns TRUE if successful.

If you need more detailed information you have to use LWP::UserAgent:

use strict;
use warnings;

use LWP::UserAgent;
use HTML::SimpleLinkExtor;

my $agent = LWP::UserAgent->new;
my $extor = HTML::SimpleLinkExtor->new('http://www.perlmonks.org/');

$extor->parse_url('http://www.perlmonks.org');

print "Checking $_: ", $agent->head($_)->code, "\n" for $extor->links
[download]

This will give you the HTTP status code. If you replace ->code by ->message, you get a human readable message instead of the three digit code.