The part of this that makes it difficult to apply the conditional validation is that the selected value comes from a select list. Since you are trying to validate a select list you will only have two client side validations available that you can use to trigger the conditional validation response. The two that are available are required, which won't work here since all of the choices in the state select list have a value associated with them, and regular expression. This one is probably the best fit, but you will need to come up with a regular expression to match for the NY selection.
You can then use this validation as the trigger for the conditional validation on the county select list.
