My girl friend is 20 and her father has never paid a penny of his child support. Can she take him to court for money for college or back pay?

If your girl friend's mother filed for child support and the father hasn't paid it, the mom will need to collect it (if the order was from the Family Court) or speak to Child Support Services (if the order was with Child Support Services) as they would be the agency who collects. In either case, it is the mom who gets child support, not your girl friend.  The mom would be the one to receive the money and use it as she feels is appropriate.