A couple thoughts come to mind. First of all, you're better off to be in the habit of using 3-argument open, because it protects you against weird filenames. This shouldn't be a problem in that case, but it's just a good habit. Also, use warnings; as well as using strict. Most importantly, your open commands should also have or die "open failed: $!" (or something similar) at the end, so that if they fail you know about it. In this case, if you try to open a locked or read-only file for writing, it will die (because open returns 0 if it can't open the file) instead of continuing on and silently failing on all its print statments, which is what's probably happening to you.

#!/usr/bin/perl -w
use strict;
use warnings;

my $readfile = "C:/Documents and Settings/mydir/Desktop/TARGETING.gb";
my $writefile = "C:/Documents and Settings/mydir/Desktop/TARGET.gb";

open my $in, "<", $readfile or die "couldn't open $readfile: $!";
open my $out, ">", $writefile or die "couldn't open $writefile: $!";

my $state;
while(my $line =<$in>){    
    if ($line=~/^([A-Z]+)/) {
        $state=$1;        
    }
    print $out $line unless $state eq "COMMENT";
}
close $in;
close $out
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The output I produced above in Re:^3 was done using the code I wrote, so that's what drives me to look at this as a file access issue, now.