Two points:

1. A tiny change should save you big time. Instead of doing the exponential stuff of 256 every time, you should use a variable to store the current value of 256 ** k from each iteration, and next iteration just multiply it by 256, to get 256 ** (k + 1), see the code.
   
   Now the complexity is a linear function of your array size, ~ o(n).
   
   
2. After my code change, you don't need a $count any more, but I still want to mention that there is absolutely no need to use BigInt for $count, that's really really huge, is your number that HUGE?

Be careful, pack and unpack does not fit in the picture.

sub bytearray_to_bigint {
  my @array = @_;
  my $base = Math::BigInt->new('1');
  my $result = Math::BigInt->new('0');
  foreach my $a (@array) {
    $result += $a * $base;
   $base *= 256;
  }
  return $result;
}
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