Brand new iPad clicking by itself.

I quite literally just bought my iPad 2 a few hours ago, and it's having some kind of issue. After several minutes of usage it will start clicking by itself, usually in the bottom half of the screen. Just now the keyboard stopped working, and the backspace/delete button is usually the first to stop working. (Or the first time I notice it not working.) Turning the iPad off and then back on makes it work fine for another few minutes. I'd really rather not have to take my brand new iPad back to Best Buy or all the way to the Apple Store. ...I'd also rather not have to strip everything off that I just added to it.

Does anyone have similar issues, or know of any way to resolve this at home?

For an example, at one point I had general settings opened and the iPad kept clicking "Use Side Switch to: Lock Rotation" every time I switched it back to "Mute," and frankly faster than I could click "Mute." I'm not sure if I need tech support or a priest.