shrekinah,
I've been in the same situation as you. My macbook pro had a hardware issue and needed to be serviced. When I called Applecare to setup a repair, my Applecare Plan was not registered to my computer. I explained to the agent I did purchase the Applecare at the same time I bought the computer then the agent transferred me to another person ( can't remember what department) and she told me to fax in my receipt that had my Applecare Plan purchase date. After several days, I sent my computer for repair without an out of warranty cost.
Here is the Applecare Plan Information:
Can I buy an AppleCare plan for my device? - Apple Support
So I believe as long as you can prove you purchased the Applecare with in the year of the computer you should be covered. (NZ not sure). You will need to contact Apple and explain the situation. Only Apple can resolve this issue with your Applecare Plan.
Here is contact information for New Zealand.
http://www.apple.com/nz/contact/
Good luck!