Nope. You have to purcjase and register the AppleCare before the system warranty is up. Of course if you had read the information on Apple's web site you would've known this.
Also, I live in the state of Florida. Does that have an impact on my AppleCare purchase?
Due to some Florida laws, Apple does not (can not?) sell AppleCare to individuals. They only sell it to business (and organizations?) in Florida. This is also clearly stated (in the fine print maybe) on Apple's web site.
Just to disagree with the posters above. I've read that in Florida, you can buy Applecare, but you'll need an out of state address to register. However, this is a moot point for you since you've missed the 1-year deadline.