I had a customer of an old company of mine send me an email effectively saying she bought a game in 2002 and has played it every day since then, and loves it, etc. But when she moved to a new Mac, she lost her registration code, so could I please either send her the code or REFUND HER MONEY IMMEDIATELY.
Did you pay for the iPad with a credit card? Check with your cc provider: most ccs come with an automatic warranty extension, doubling the original warranty up to an additional year. Check the fine print – might save you some cash.
They routinely replace out of warranty iPads as a one-time courtesy. My iPad 2 had the screen smashed and they just replaced it, when all I was doing was inquiring about a repair.
Seriously, as several people have already told you, unless you just want to “take it up the popper” for some reason, take it back to the store. It’s been my experience that if something they make breaks through no fault of your own, they are very likely to just replace it for you. With the iPad / iPhone, this policy seems to have been formalized (but not published), and includes accidental damage.