NROTC without Scholarship?

I want to be an officer in the Navy. I want to be a computer programmer within it. I'm really trying to get into Anapolis or the Scholarship but I don't think I will. I am worried that if I don't get the scholarship and go into the Navy as a comissioned Ensign I will not have enough money to pay back my student loans by the time my first enlistment is up (four years to pay it off but i'll probably serve more)? I really want to go to the Navy to carry on the tradition of my family but I don't want to have to serve while figuring out how to pay for my student loans and still having them when I go into the private sector. Schools I would be looking at would be Pitt, Penn State, and University of Arizona (approx. 20k/year). I don't want to sound like I'm only doing this for money. If I was I would not be considering doing ROTC while not on scholarship. I want to serve my country but I am very worried about paying for college. I don't want my parents to have to pay a cent because its my education not theirs. Thank you for all serious answers on whether it is doable or not and the best course of action.