A eunuch is a man who has been castrated. A person with (partially) both male and female genitalia (sex organs) is an hermaphrodite.
I am not aware of any condition where a person is born so devoid of any sexual characteristics that they would not be termed one or the other. The only other word I can think of is 'asexual', which is a term used about organisms, in biology.
Anyone else able to clarify?