The battery on an iPad 3 should still be covered by Apple's 1-year warranty. Could be a defective wall charger. Are you using the wall charger or USB on your computer?
Take it to an Apple Store for evaluation.
Make a Genius Bar Reservation
Well last time i checked it was somewhere around $100. If you are gonna spend that much though i suggest buying one of the iPad cases that charges using solar power so that you don't really ever have to change the battery and they are only like $200 which will probably save you $100 in the long run.