my $regex = '\w+(ATG\w*T(AG|AA|GA))\w+';

Going wrong:

• The  $regex you have defined matches the entire string! You then take this match (the entire string) and feed it to  find_coding() again: deep recursion. (Update: See this for more detailed discussion of recursion problems.)

  c:\@Work\Perl\monks>perl -wMstrict -le
  "my $inputseq = 'AATGGTTTCTCCCATCTCTCCATCGGCATAAAAATACAGAATGATCTAA';
   print qq{'$inputseq'};
   ;;
   my $regex = '\w+(ATG\w*T(AG|AA|GA))\w+';
   $inputseq =~ /($regex)/g;
   print qq{'$1'};
  "
  'AATGGTTTCTCCCATCTCTCCATCGGCATAAAAATACAGAATGATCTAA'
  'AATGGTTTCTCCCATCTCTCCATCGGCATAAAAATACAGAATGATCTAA'
  [download]

• A small point: Please don't define regexes as strings: A number of subtle bugs can be encountered. Use  qr// (see perlop).
• Another small point: Please try to avoid using capturing groups in  qr// objects (especially absolutely unnecessarily, as in this case). It makes counting groups at the top level a headache.
• Please define what you mean by "... all possible DNA sequences ..."

Update: Several small edits for clarity and de-typo-ization.

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