Who governs or is in charge of pressuring Elementary schools?

My son's elementary school has found "no problem" with him and has found him not to be in need of special services. I have just received preliminary results that he does qualify for special education services from independent testing. All this despite hiring an advocate (admittedly a poor one). Who can I go to within the system that will put pressure on the school (Principal) to buck up the money? My son deserves the special services and we pay taxes for just this reason. Now, I'm even wondering if the District Board of Ed puts pressure on the Principal to not spend. It's been so sickening to find that whomever screams the loudest will get the services and that schools don't want to spend and push those in need aside if they think they can get away with it. I want to put extreme pressure on this Principal so that she gives my son what's due him quickly and inexpensively without having to wait and pay for private testing and until next year. I'm at the point where my next step is to hire a lawyer as the advocate didn't threaten them into complying with what's right at all. Will the district level be enough ? Do I have to go to the state level? Is there an external agency that would help? Thank you in advance.