For what it's worth, hearing can be tested fine, but there is an auditory disorder (I can't find what it was called) wherein someone will hear you, but not process any instructions because of a disconnect between the auditory functions and brain processing. It's just like background noise to them. They have to be looking right at you for them to "hear" you.

Also, a buddy of mine had a ton of trouble when he was young. He didn't start speaking until 3 or 4, didn't interact with the other kids in a normal way ... a lot of what you are describing. His problem wasn't that he had a mental illness or learning disorder though.

His problem was he was freaking brilliant. He was very cerebral at that young age and as he got older, decided that communicating was an okay thing to do and now he's very social (and a chemical engineer that graduated 4.0 GPA).

You say he understands his numbers (my kids always had one they skipped for some reason too) and you say you know he "knows" something. I wonder if he hasn't already figured it out and gone on to the next thing? Like you sent him for the window cleaner and he knew where it was and blah, blah ... he was bored and dropped the idea.

So there could be some other rather obscure things going on. And once in a while when we think something is "wrong" it's actually gone horribly right!