Why can't I change the screen orientation of my iPad?

Of course that was the first thing I tried (I refer to that in my original post--that was what I meant by turning the lock feature on and off).

I should also say that I tried restarting my iPad, to no avail.

Unfortunately not. I found a work-around that allows me to use the device in landscape format. I use the accessibility settings in settings (under general) and turn "assistive touch" on. A white dot appears on the screen. When you click on that, you can rotate (and lock) the screen in any position you like.

It's not ideal, but so far it's all I've got. I'd like to bring it into a genius bar, but haven't had time.