As far as I know, if you keep a copy of the invoice, we can usually use that for the warranty date in the U.S. as long as it's from an 'authorized reseller' (used or second-hand items would not reset the warranty start date, etc.), so that should give you a little more time.
Otherwise, if you lost or don't have the invoice, we should be able to check the 'manufacturer' warranty from the serial number.
If you have the interest, contact ASUS support and give them your serial number to find out how much warranty you have (and ask if you need to register while you are at it?) which would be the manufacturer warranty without the invoice.
Then contact them again or reply to tell them you have the invoice and give them the details of whom it was purchased from and the invoice purchased date to find out your warranty with the invoice if you're interested.
Not sure if all the other regions follow the same process, but expect many do since products do sometimes sit in the warehouse for a while before being sold.