Arnold was certainly paying to support the child either through wages or other help to the housekeeper/mother, but it would still be the case that the child thought he had ‘never had contact’ with his NCP and when he went to fill out the CSS would state "I have no contact with my father’ and honestly believe that. In this case, if the OP has no contact, that doesn’t mean that the father has no ability to pay. He may have developed quite a career by now, have won the lottery, have invented something.
It happens all the time that the CP wants nothing from the NCP except from him to get lost. Usually state/fed aid agencies and universities are more anxious for the NCP to be a little uncomfortable and pay up.