I'm not sure if you said claiming your daughter as a dependent gave you no benefit -- it should get you the $500 credit for other dependents.
That aside, if your daughter was 19 and NOT a full time student, and you do not claim her as a dependent on your return, then she would qualify for the Refundable portion of the AOC.
If she is 19 and is a full time student, none of the refundable credit can be claimed.
In no circumstances can the non-refundable credit be claimed.
