Broken iMac screen

Even if you had purchased AppleCare it would have expired in 2013. Even if you had active AppleCare, Apple does not cover accidental damage only manufacturing defects.

Your only chance is if you have Earthquake insurance and check with the insurance company if they cover the expense, otherwise the repair will be at your expense. However you can do the work yourself, the glass is only held in by magnets. You should be able to locate a screen on E-bay and install it yourself. You can find many videos online (try Youtube) that show how easy it is to do.