There are a few replies that give this same recommendation, so a nod to those as well... but this was the one I followed and it worked great.
We've got lots of iPads, iPhones, and iPods floating around the house, with older models getting passed to the kids when we upgrade at the top. Kick in the conspiracy theories, because I was seriously thinking that, when the iPad 2 my daughter uses got bricked by the 9.3 update, that maybe it was time to buy a new iPad for me and pass my "old" one down the line. Sounds like a good excuse, actually, but I didn't want to lay out the cash right now.
Then I thought to give a search for others with the same problem, and lo and behold it's everywhere:
The 9.3 update is definitively bad for at least some iPad 2 owners. Maybe even more than just a few.
I did the DFU restore before, reinstalling 9.3 from scratch and copying over a backup (thank God I had one). It worked... and then it didn't. My daughter was midway through using the device and it reverted back to the failed activation screen.
So last night, I followed gino55's steps and downgraded to 9.2.1. I let it sit overnight while it restored the backup, to alleviate some of the pain of waiting through that again. This AM it was back to functioning, by all appearances, just fine. We'll see if it crashes to the activation screen again, but my guess is no.
I'm sure Apple will come out with a fix as soon as possible. But if you don't want or can't afford to wait, try the steps above.
They do work.