Not really golfing here, but there's far too much code in that last subroutine.

sub build_board_array {
  my @board = split //, shift;
  s/Q/Qu/ foreach @board;
  @board = map {
    +{ line => [map +{ letter => $_ }, splice @board, 0, 4 ]};
  } 1..4;
  return \@board;
}
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-- Randal L. Schwartz, Perl hacker
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UPDATE: oops, forgot one arrayref constructor.