This can be resolved by filing a Non-Resident Virginia tax return to claim a refund of all withholding taxes paid to them. Then, file your New York return (or returns, if you have city returns also) as you normally would.
It's most likely you will owe New York because there was no withholding, but you can use the Virginia refund to pay the taxes if you file in time for the refund to be processed before your payment is due to New York.
