I think I see some problems. In

while (<FILE2>) {
  push @col, $_ =~ m/^(\S+)/  unless ...;
}
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you probably want to say my @col, otherwise @col keeps accumulating stuff from the previous pass through the first while loop.

Likewise, in

while(<COL>) {
  $_ =~ s/^(\S)/$1 $col[$i++]/;
  print OUT2 $_;
}
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you probably want to say my $i++

so $i starts at 0 again, instead of being left with whats in it from the while (<COUNT>) loop.

And again, in

while (<COUNT>){
  ($i, $j) = ...
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it would be good if you used

my ($i, $j)
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You also create and destroy the TRUE_OUTPUTS file each time through the loop. But from what you've shown, it never changes. So it would be better to put this at the top:

open (FILE, "test.pat") or die "Can't open test.pat: $!";
open (OUT, ">TRUE_OUTPUTS") or die "Can't open TRUE_OUTPUTS: $!";
while (<FILE>) {
  if ($_ =~ m/^\s{4,}(\d)\s+$/) {print OUT "$1\n"}
}
close (FILE);
close (OUT);
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Note that I used a constant "test.pat" since you said that doesn't change. I also added die and tidied up the regex by using {4,} to match 4 or more.

Also, you forgot the die in

open (COUNT, "<COMPARE") or "Can't open COMPARE: $!";

And now, just to be nitpicky, $output seems like a bad variable name. I think $input_file or just $input would be better.

Hope this helps.

TheEnigma