Hi,
I have the same problem with my nearly new iPad. I upgraded to iOS 8.3 and after that the apple logo flashes at least ten times during the reboot process.
Finally it starts working but the apple logo appears again and again randomly, it seems like a reboot, but disappears 5-10 seconds later. It isn't in connection of using any of application on it, and immediately appears every time when I go into the Setup and try to change anything there (for example).
The restore and the recovery didn't help.
I was afraid that my device's broken, but I see now, it was the upgrade what caused the problem. (otherwise so many iPad's broken in same way at nearly same time which is hard to believe.
We are waiting for Apple to fix the problem. Thank you.
K.