No you can file a PayPal dispute anytime, GIVEN
that you sent the money as a payment and NOT
as a gift. If you sent it as a gift, tough shit there isn't anything PayPal can do for you seeing how they tell you that funds sent as a gift are non-returnable. If you sent it as a Payment, you can open a claim against the item and if in 7 days you haven't worked it out, you may open a dispute. PayPal will look over the dispute and reward the case to one of the two parties. If the guy doesn't provide any response at all, you will obviously win the case and your money will be refunded.
Hope this helps and good luck getting your money back from this asshole.