hi Berislav,
i think, you have 2 problems on your code:

1. for ($lb=0; $lb<length $dna; ++$lb), the lenght of the array must be length($dna) -1 (the last elemet cannot be compared with anything ... perl accepts this, though)
2. the 'tr' only tries to convert between lowercase letters. The example you gave us have uppercase letters ... the result isn't the same ...

I've retouched your script, so the problem of the large string will not affect you

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

system "clear";
print "Palindrome - gamma version\n";
print "--------------------------\n\n";
print "Please enter DNA filename: ";

my $filename=<STDIN>;
chomp $filename;
die "No such file...exiting\n\n" unless (-e $filename);
open(DNASEQ, $filename) or die "Cannot open file...exiting\n\n";

my $last_protein;
my $count_of_2=0;
while (<DNASEQ>) {
        chomp;
        my ($lba,$rba)= ($last_protein, undef);
        for (my $lb = 0; $lb < (length) - 1; ++$lb) {
                $lba  =  substr ($_, $lb, 1);
                $rba  =  substr ($_, $lb+1, 1);
                $rba  =~ tr/atgcATGC/tacgTACG/;
                ++$count_of_2 if ($lba eq $rba);
        }
        $last_protein = $rba;
}
print "Number of 2bp palindromes: ", $count_of_2, "\n";
[download]

hope that helps :-)