First... Don't be afraid to root... It's not brain surgery or anything like that and you can root and run completely stock if you choose to. Rooting actually helps make trouble shooting and fixing things a bit easier in the long run. Just makes your Tab a bit more flexible and alot more useful.
Anyway... So your completely stock, unrooted and on the latest ICS.
Now you said you were using an app like normal and your Tab just shut down. And when you went to restart it it gets hung on the Samsung boot screen with the flashing halo around the word Samsung.
When you reboot your Tab it should first come to a splash screen that says "Samsung Galaxy Tab 10.1" then the next screen you'll see is the animated "Samsung" screen. That screen comes up when the actual os starts to boot up.
I'm not real sure why but something is not allowing the OS to boot. It could and most likely is an app that you've downloaded, let's hope that's all it is.
I know your most likely not going to want to hear this but your first course of action should be to try a hard rest from the stock recovery. If you were to call Samsung to trouble shoot this its what they would tell you to do. It sucks and yes you will loss all of your user data, setups and music, videos and pictures... but it could get you up and running again and that should be your first concern.
So to do a hard reset:
1. Turn your Tab off.
2. Hold down the volume down button and tap the power button to turn your Tab back on.
3. Keep holding the volume down button until you see a screen with 2 icons on it. The one on the left should be a little android guy standing next to a box and the one on the right should say download... When you see this screen you can let go of the volume down button.
4. Now you want to select the icon on the left... To do this just tap the volume down button once, the android/box icon should be highlighted.
5. Once you've got the left icon highlighted, tap the volume up button to accept or choose that icon.
This should boot you into the stock recovery... Now I'm shooting in the dark here a bit, in haven't seen a stock recovery in about 2 years so.... But what your looking for is an "wipe" option. If I'm remembering right there aren't the may choices to choose from so you should be good. You use the volume keys to highlight it then the power button to make your choice.
This will reset your Tab back to its factory setup (except you should still be on ICS I think) just like out of the box.
Give this a try and report back and let me know what you get.
Sent From My GalaxyClass StarShip