Te only thing you can do is take the system and the AC charger to Apple and have them look at it. If they determine the power cord damage is from a manufacturing defect they will replace it under warranty. If they determine it is from User Abuse, whether it is or not, then they will not replace it and you will need to buy a new one.
Do you have any animals in the house, like a cat? If so it may be that beast that caused the damage. Cats seem to love the Apple AC charger cables.
Since you're still under warranty, I would take the whole kit (including adapter) into your local Apple Store or an AASP and have them diagnose your problems. Don't know why you're having those sleep issues, but if you haven't been too rough with the adapter, you should get a free replacement (unless the Genius you get is convinced that it's user damage).
Good luck - take advantage of your warranty...