I think you are attacking the problem from a wrong angle. You are walking through your DNA string step by step, instead of jumping through it in increments of three. Also you are using a C-style loop, which is very error prone, in your case for example the first element of @dna is at $dna[0]. I'd rewrite your code in the following way, jumping forward three slots with every round :

use strict;
my $i = 2;

my @dna = split //, 'CTCCGGATCTAT';
my $counter = 0;
my $total = 0;

while ($i < @dna)     {
   if ($dna[$i] eq 'C')    {
          $counter++;
    }
   elsif ($dna[$i] eq 'G')   {
          $counter++;
   }
   $total++;
   $i += 3;
 }
print "Found $counter G/C of $total elements at a 3-position\n";
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perl -MHTTP::Daemon -MHTTP::Response -MLWP::Simple -e ' ;    # The  
$d = new HTTP::Daemon and fork and getprint $d->url and exit;#spider
($c = $d->accept())->get_request(); $c->send_response( new   #in the
HTTP::Response(200,$_,$_,qq(Just another Perl hacker\n))); ' #  web
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