Please, just ask this question first: Was this tuition paid for you, your spouse, or a dependent? If no we are done, it does not qualify. It could be that simple on the federal as well as the New York return.
In the section on tuition deduction in New York State, Turbo Tax asks for name SSN DOB and then dependent type. If one answers Other, ie. not a dependent, the deduction is not allowed, but turbo tax goes on to chase you around for University name and EIN and doesn't tell you don't qualify until later.