Why won't here1 and here2 showup on the output?

Because your program doesn't compile, it cannot be run, and thus it cannot output anything.

$ perl -e'
   use strict;
   use warnings;
   print "here1\n";
   @files = <*>;
   foreach $file (@files){ print $file . "\n"; }
   print "here2\n";
'
Global symbol "@files" requires explicit package name at -e line 5.
BEGIN not safe after errors--compilation aborted at -e line 5.

$ perl -e'
   use strict;
   use warnings;
   print "here1\n";
   my @files = <*>;                                  # <-- my
   foreach my $file (@files){ print $file . "\n"; }  # <-- my
   print "here2\n";
'
here1
Build.PL
Changes.txt
inc
lib
LICENSE.txt
MANIFEST
MANIFEST.SKIP
README.txt
t
here2
[download]

...and that is considered ancient perl syntax. Do this instead:

use strict;
use warnings;
use 5.010;

for my $file (glob '*') {
  say $file;
}
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There's nothing ancient about using the diamond operator for globing. As in this case the wildcard processing is actually not needed, it'd probably be better to use opendinr&readdir as that doesn't put the whole list of files into memory at once, but that doesn't really matter in most cases.

Jenda
Enoch was right!
Enjoy the last years of Rome.

#!/usr/bin/perl

use strict;
use warnings;
use diagnostics;

open(LOG, '>', '/root/Desktop/log.out') or die "Can't redirect stdout:
+ $!";
open(CMD, 'ls |');
open(STDERR, '>&', STDOUT) or die "Can't redirect stderr: $!";
open(STDERR, '>', 'LOG_FILE') or die "Can't redirect stderr: $!";
print "\nhere1\n";
while (<CMD>) {
    print_stuff ($_);
}

sub print_stuff {
      my ($line) = @_;
      print LOG $line;  
      print $line;
}
print "\nhere2\n";
close LOG;
close CMD;
close STDERR;

exit;
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