I'd recommend you check out woolfy's Where and how to start learning Perl as there are some strange assumptions here, but a possible rewrite:

use strict;
use warnings; #good!
use Win32::OLE;
use Date::Calc; why load when you don't use it, or Win32::OLE?

#having a few variable with a large lexical scope isn't  
#nessarily bad but in general use the smallest scope

# This acutally assigns the file location to a scalar
# doesn't get anything (as [holli] stated)
my %header_data;
my $f_mfg_desk = '//163.../chicago_wip_query.txt';

# Since you don't actually use @headers: I dropped it
# If you needed it just say why and I'll go from there

# "time" gives seconds after epoch which is proably not what you want,
+ see localtime*
my ($sec, $min, $hour, $dayofmonth, $month, $year, $weekday, $day) = l
+ocaltime(time);
$month++;
$year += 1900;

open (INFILE, $f_mfg_desk);
#if you do my $record = <INFILE> you'd need chomp($record);... or
while (<INFILE>)
{
  chomp;
  my @newrow = split /\t/;
  #missing the ]; here
  $header_data{$newrow[2]} = [ $newrow[3..18] ];
}
close(INFILE);

#to sort and reprint (proably want to copy a backup too)
open (OUTFILE, ">$f_mfg_desk");

# see perldsc* and sort*
for my $key (sort keys %header_data)
{
  #see perlref* for @{}
  for my $a (@{$header_data{$key}})
  {
    print OUTFILE "$a\t";
  }
  print OUTFILE "\n";
}
[download]

*:localtime, perldsc, sort, perlref