All of this is assuming, of course, that you are passing a value to $input. You didn't really specify how you were parsing the form results. One way is the following:

#!/usr/bin/perl -w

use CGI;
use strict;
my $page = CGI::new();
my $input = $page->param('checkbox1');
if ($input eq 'on') {
    # do something
} else {
    # do something else
}
exit (0);
[download]

with the HTML set like the others have suggested, giving a value of "on" to the checkbox named "checkbox1".