Correction: 15" screens were never offered on iBooks. Current sizes are 12" and 14".
If I'm not mistaken, you cannot purchase AppleCare after the product's factory warranty (1 year parts/labor) has expired. Furthermore, AppleCare doesn't cover abusive and/or incidental damage done to screens (I've seen them make some exceptions, but not many). I know this because my buddy at school tripped over the power cord on his pretty new 15" AlBook, which fell to the floor with the screen open, cracking the LCD and bending the hinges. It's now on its way to Apple for a $700 repair not covered under warranty.
Outfitting an iBook with a different screen than OEM specification would be highly impractical, if not impossible. First of all, the graphics chipset and driver are specifically customized by the laptop's manufacturer (i.e. Apple) to work optimally with the display the laptop is equipped with. That display has a specific native resolution and refresh rate that the graphics hardware needs to compliment.
What kind iBook do you have? Apple actually offers
flat-rate repairs for stuff like this, but depending on the age of the iBook, it might be cheaper to buy a new one.