Hi J.,
I'm a single mom who has also gone through all of the legal channels (and still have over $5K left to pay in legals fees, ick).
You said that your friend's son's father is legally bound to financially support his child - does she have a court order? She should have SOMETHING that was filed with the circuit court clerk. It will he stamped with the time and date. I'm not sure if you meant her former lawyer or the courts when you mentioned "powers that be" - but if she had something filed with the court it will make the task of collecting support easier. If she doesn't have any kind of court-stamped documentation (but it exists) she will need to go to the clerk of the court and get a copy - which there will be a fee for.
If she doesn't have a court order signed by a Judge.... then her son's father doesn't owe her a cent (yet)... it's all about the paper trail (I've learned that the gard way myself!)