$i was being clobbered as psini pointed out but this was only one major problem. The second problem is that your filehandle 'DIR' is getting clobbered. I think that the program still is not working correctly. To demonstrate:

open FH, "<foobar" or die;
my @stats = stat FH;
print "First inode ", $stats[1], "\n";
{
   open FH, "<foo" or die;
   my @stats = stat FH;
    print "Second inode ", $stats[1], "\n";
}
@stats = stat FH;
print "First inode ", $stats[1], "\n"; # FH has been clobbered.

__END__

....
First inode 683751
Second inode 684162
First inode 684162
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