While certainly not shorter than other posts, I believe the following provides what the OP is looking for.

#!c:\perl\bin\perl.exe

use strict;
use warnings;

my @comments;
my $i;
my $j = 0;
my $found_comment = 0;
my $input = 'c:\yourdirectoryhere\sample_perl_data1.txt';
my $line;

open(IN, $input) or die("Can't open file - $input: $!");

while($line = <IN>) {
   if($line =~ m/^=/) {
      if($line =~ m/^===Comments===/) {
         $found_comment = 1;
         if(! defined $i) {
            $i = 0;
         }
         else {
                $i++;
         }
         $comments[$i] = "";        # initialize new comments array el
+ements
      }
      else {
         $found_comment = 0;
      }
   }
   else {
      if($found_comment == 1) {
           $comments[$i] = $comments[$i] . $line;
      }
   }
}
close(IN) or die("Unable to close file - $input: $!");

#print output with a separator line between each element
for($j=0; $j<=$i; $j++) {
    print("comments[$j] = $comments[$j]");
    print("------------separator-------------------\n");
}
[download]

Update:

Sample output below:

comments[0] =
User comments are added here. A user may write whatever they may wish.

------------separator-------------------
comments[1] =
Comments are related to the microarray data here.

------------separator-------------------
comments[2] =
Comments related to the pathway information here.

------------separator-------------------
[download]