2 month old iPad - they'll most likely refer you to the Apple store. And I don't blame them either... Apple doesn't make life easy for retailers at all.
The law doesn't make life easy either. The retail store is legally obliged to deal with the issue.
Having said that, it may be quicker to deal directly with Apple.
Take it to an Apple Store.
You can quite happily take it to any Authorised Repair Centre, but why would you if you do have access to an Apple store.
Book an appointment at Apple Retail Store with a Genius Bar at a store near you for your iPad. Take it in, they'll see it's dead, and chances are, replace it on the spot. They keep separate stock of Service models to Sales models, so whilst they may not have stock available for sale, chances are they'll have Service stock.
The Genius Bar are a much easier solution than service centres if you can manage it.