Apple seems to be a bit pickier these days.
You at the minimum would have 1 year from the date of the original sale. Not to you that it, but the very first sale if it was registered with Apple. Not all are in which case you may start from day 1. Don't hold your breath for that. The warranty goes with the machine. If it's within that period, you can also buy the Applecare addition to extend the warranty.
Apple used to be pretty good about resetting the warranty date on an open box, they've done it for three of mine, but seems they're not so gracious anymore.