Very strange behavior, can't reset, can't turn off!

I was starting to download some digital magazines I'd checked out from the library using the Zinio app. When I started, the screen flashed for a second and then the screen went black and the animated Samsung logo popped up like the tablet was powering down, or like you see when powering up. The only problem is that it's been that way for about a half hour now. It's not doing anything that I can see. I've tried to power down and it won't shut off. I've closed the magnetic cover, and it won't go to sleep. I've tried the volume up/power button reset, and that does nothing. I guess it's just going to stay like this until the battery dies completely. Has anyone ever seen behavior like this? Any ideas?

Thanks for any advice or opinions.

- Byron

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