Not sure if this is much better than your code:

#! perl -slw
use strict;

my %invert; @invert{ qw[ A C G T ] } = qw[ T G C A ];

my $in = do{ local $/; <DATA> };
chomp $in;
print $in;

for my $p1 ( 1 .. length( $in ) -2 ) {
    next unless substr( $in, $p1, 1 ) eq $invert{ substr $in, $p1+1, 1
+ };
    my $pals = 0;
    for my $p2 ( 1 .. $p1 -1 ) {
        last unless substr( $in, $p1-$p2, 1 ) eq $invert{ substr $in, 
+$p1+$p2+1, 1 };
        ++$pals;
    }
    if( $pals ) {
        printf "%s%s at %d\n", ' 'x($p1-$pals),
            substr( $in, $p1-$pals, ($pals+1)*2 ), $p1-$pals;
    }
}

__DATA__
AGAGGTCAGTCTGCATCGTATCGATCGTCGACGATCGATACGATGCAGACTGACGAGAG
[download]

Produces:

[13:44:54.28] C:\test>1085446
AGAGGTCAGTCTGCATCGTATCGATCGTCGACGATCGATACGATGCAGACTGACGAGAG
           TGCA at 11
                   ATCGAT at 19
                     CGATCG at 21
    GTCAGTCTGCATCGTATCGATCGTCGACGATCGATACGATGCAGACTGAC at 4
                               CGATCG at 31
                                 ATCGAT at 33
                                           TGCA at 43
[download]

Modify to taste :)

I know nothing of this, but simply did a search for "CPAN panindrome" and came up with:

• This

and

• Another(applicable?)

If the output is unclear, clarify it. (Is this your code?). I agree with the previous response in getting rid of the 'goto'.
Other than that, if it works... .

Honestly, unless this is a code writing exercise, I would look for something already written and freely available. Even if it is an
exercise in code writing, look at what has been written and use that as an example.

Hope that is helpful...

      if ($start == 0)
         {
         goto NEXTLINE;
         }
[download]

next NEXTLINE if $start == 0;
[download]

Perhaps you already know this but DNA palindrome is a fairly casual way of saying inverted repeat. Not trying to be picky but the latter term should help with the search.

With this in mind, BioPerl has an interface to the relevant function of the popular (and huge) EMBOSS package.

Possibly a bit too narrow but you might also want to take a look at a recent paper which uses a Perl script to find a particular type of inverted repeat (MITE).

Many apologies for the delay in replying to this thread. As per the advice above i've decided to make use of existing biological tools (EMBOSS) and wrapping this in bioPerl to get a suitable output format rather than constructing something from scratch. I will post the solution when it's completed and also explain it for non-biologists to answer the questions below. Thanks again!

open (TEXT, "sample.txt")||die"Cannot";
...
NEXTLINE: while ($count < 1000)
    {
    $line = <TEXT> ;
    $count++;
    foreach my $value (@regexes)
       {
       ...
       while ($line =~ /$value/g)
          {
          ...
          }
       ...          
       }
    }
...
[download]

If the file you're reading has fewer than $count-limit lines, the loop will continue to operate on an undefined value of  $line until  $count reaches its limit. (I tried the code on a file with the single DNA sequence included in the OP with interesting results.) I suggest adding a test after the file read:
    $line = <TEXT>;
    last NEXTLINE unless defined $line;

Use of warnings would have allowed Perl to alert you to what was happening. Use of strict is also highly recommended, but would necessitate several further changes to the code.

As a non-bio-monk, there are several questions raised in my mind by your post and by BrowserUk's reply above. With luck, they are trivial questions, and you can easily direct me to answers.

BrowserUk's solution produces the 50-base palindrome shown in the OP, but also produces other sequences that seem to be palindromic (again, to this bio-naif) and that are "embedded" within the longer sequence. Are these other sequences significant? Do you want to know about all, some or none of them?

In broader terms, consider the sequence
    ...CGATCG...CGATCG...CGATCG...
where ... represents zero or more bases that do not participate in any palindromic relationship. CGATCG is itself palindromic, each pair CGATCG...CGATCG presents another relationship (possibly more than one?), and the entire sequence presents...? Again, which of these seeming possibilities are significant? Which do you really want to know about?

I assume you are a biologist or are involved in biological computation, so these questions are probably pretty mundane. I hope it will not be much trouble to set me on the path to enlightenment.

Are these other sequences significant? Do you want to know about all, some or none of them?

(2) Be able to specify a minimum and maximum length of match

---

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Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority".

In the absence of evidence, opinion is indistinguishable from prejudice.