SWOT, around here, health & human services will ONLY deal with this sort of thing if you are indigent (and have jumped through ODJFS hoops for TANF and other assistance) or have been referred by the legal system. Since we don't qualify for the first, we have to go the second route.
That said, we HAVE gone the private route, had insurance (help) cover the original neuropsychologist evaluation. However, since ACA, now we are required to get a referral from the pediatrician. I barely managed to wrangle one out for Auditory Processing Disorders (APD) testing... In the kids' practice, there are a couple of docs I could happily do without. If the others weren't so darned GOOD - but I digress. I have set the kid up with 2 different well-child checks (with the docs I like, so I had to wait for appointments of course), both of which he missed - one because he just didn't ride the bus home from school and we couldn't find him (Bill was supposed to take him), the other when he refused to go and walked out (that was me, and I can't physically stop him). Insurance doesn't cover missed appointments and there is a $75 charge each time.
The biggest issue here is helping someone who refuses to help himself. I can work myself blue in the face, but since he presents as a perfectly normal kid... Yep.
I despise not being able to do anything.