Thank you. Turns out on my system, taint is a capital T. I also added the extra lines after header as suggested by DapperDan. Here's the resulting code plus some recent data, but all I get as output is "-: 1". Not sure why.

#!/usr/local/bin/perl -slwT

use strict;
use warnings;
use Date::Manip;
use CGI qw/:standard/;

# Make sure neither we, nor any of our submodules compromise security
# by calling unpathed programs.
$ENV{PATH} = "/bin:/usr/bin";
$ENV{IFS}="";

# Use CGI to print our headers
print header, "\n\n";

my %referers = ();

# Retrieve and security-check parameters
my $hour = param('hour');
my $minute = param('minute');

if ($hour !~ /^\d\d?$/) { die('Invalid hour'); }
if ($minute !~ /^\d\d?$/) { die('Invalid minute'); }

# Get date object for our check point
my $check_date = ParseDate("${hour}hours ${minute}minutes ago");

# File handling, one line at a time
open(FH,"datafile.html") || die('Could not open log file');
while (my $line = <FH>) {

    next if ($line !~ /^\S+ \S \S \(\S+) \S+\ "^"+" \d+ \d+ "(^"+)"/);
    
    my $line_date = ParseDate($1);

    # Check to see if the line date is in the range we're after
    next unless Date_Cmp($line_date, $check_date)>0;

    # If the referer is new, we set to 1 entry, otherwise increment (incrementing undef doesn't work well)
    if (!$referers{$2}) {
        $referers{$2}=1;
    } else {
        $referers{$2}++;
    }
}
close(FH);

my $row = 0;

# Sort our referers by the number of hits
for (sort {$referers{$b} <=> $referers{$a}} keys %referers) {
    # break out after the tenth one
    last if $row++==10;
    print "$_: ".$referers{$_}."\n";
}

Recent data:

68.22.179.211 - - 15/Dec/2002:14:52:13 -0500 "GET /images/69.gif HTTP/1.1" 200 1348 "http://www.indystar.com/print/articles/6/008596-6466-040.html" "Mozilla/4 .0 (compatible; MSIE 5.5; Windows 98)"
141.154.123.193 - - 15/Dec/2002:14:52:13 -0500 "GET /images/header_aod2_01.gif HTTP/1.0" 200 2011 "http://www.indystar.com/print/articles/2/008227-9652-031.ht ml" "Mozilla/4.79 en (Windows NT 5.0; U)"
141.154.123.193 - - 15/Dec/2002:14:52:13 -0500 "GET /images/header_aod2_15.gif HTTP/1.0" 200 4162 "http://www.indystar.com/print/articles/2/008227-9652-031.ht ml" "Mozilla/4.79 en (Windows NT 5.0; U)"
141.154.123.193 - - 15/Dec/2002:14:52:13 -0500 "GET /images/header_aod2_10.gif HTTP/1.0" 200 3034 "http://www.indystar.com/print/articles/2/008227-9652-031.ht ml" "Mozilla/4.79 en (Windows NT 5.0; U)"
141.154.123.193 - - 15/Dec/2002:14:52:13 -0500 "GET /images/go_blue.gif HTTP/1 .0" 200 133 "http://www.indystar.com/print/articles/2/008227-9652-031.html" "Moz illa/4.79 en (Windows NT 5.0; U)"
141.154.123.193 - - 15/Dec/2002:14:52:13 -0500 "GET /images/aod_searchend2.gif HTTP/1.0" 200 186 "http://www.indystar.com/print/articles/2/008227-9652-031.htm l" "Mozilla/4.79 en (Windows NT 5.0; U)"
24.79.125.220 - - 15/Dec/2002:14:52:13 -0500 "GET /images/coheader2_aod_08.gif HTTP/1.1" 304 - "http://www.indystar.com/forums/showthread.php?s=&postid=177044 " "Mozilla/4.0 (compatible; MSIE 6.0; Windows 98; Win 9x 4.90; Q312461)"
24.79.125.220 - - 15/Dec/2002:14:52:13 -0500 "GET /images/coheader2_aod_10.gif HTTP/1.1" 304 - "http://www.indystar.com/forums/showthread.php?s=&postid=177044 " "Mozilla/4.0 (compatible; MSIE 6.0; Windows 98; Win 9x 4.90; Q312461)"
141.154.123.193 - - 15/Dec/2002:14:52:13 -0500 "GET /images/email.gif HTTP/1.0 " 200 138 "http://www.indystar.com/print/articles/2/008227-9652-031.html" "Mozil la/4.79 en (Windows NT 5.0; U)"
66.149.178.96 - - 15/Dec/2002:14:52:14 -0500 "GET /forums/showthread.php?s=&po stid=177042 HTTP/1.1" 200 7302 "-" "Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1 .0.1) Gecko/20021003"
24.79.125.220 - - 15/Dec/2002:14:52:14 -0500 "GET /images/coheader2_aod_11.gif HTTP/1.1" 200 954 "http://www.indystar.com/forums/showthread.php?s=&postid=1770 44" "Mozilla/4.0 (compatible; MSIE 6.0; Windows 98; Win 9x 4.90; Q312461)"