If the format of the dates that you are getting is pretty rigid (as it seems) then Date::Manip is probably overkill.

Looks pretty simple to parse these dates into their component parts which you can then pass to timelocal to get the number of epoch seconds. Something like this:

#!/usr/bin/perl -w

use strict;
use Time::Local;

my %mon = (Jan => 0, Feb => 1, Mar => 2, Apr => 3, May => 4,
           Jun => 5, Jul => 6, Aug => 7, Sep => 8, Oct => 9,
           Nov => 10, Dec => 11);

sub parse_date {
  local $_ = shift;

  my ($mon, $day, $year, $hr, $min, $am_pm) = split /\W+/;

  $mon = $mon{$mon};
  $year -= 1900;

  $hr += 12 if ($am_pm eq 'PM' and $hr != 12);

  timelocal(0, $min, $hr, $day, $mon, $year);
}

while (<DATA>) {
  chomp;
  my ($start, $end) = split(/ & /);

  print parse_date($end) - parse_date ($start), "\n";
}

__END__
Mar 19, 2001 01:23 PM & Mar 19, 2001 03:52 PM
Mar 19, 2001 11:42 AM & Mar 19, 2001 12:21 PM
Feb 29, 2001 11:23 PM & Mar 01, 2001 12:12 AM
[download]

Doesn't handle the last one correctly, but then Feb 29 2001 isn't a valid date! Might want to check for that too :)

--
<http://www.dave.org.uk>

"Perl makes the fun jobs fun
and the boring jobs bearable" - me