Yes i have done the same with an 1phone 5C, after continuing to be reminded to update my phone to the new IOS 9.3. 1, i decided i would and had sufficient charge to do so, it has not turned on in the two days since the update. I have tried going to itunes as said above but it asks me to unlock my phone which of course i cant as it does not start up, i have also tried the other suggestions above but nothing seems to work.
There is obviously a problem with this update and a warning should be sent out if that is the case ( it obviously effects some phones and not others) . My phone is 18 months old but was working fine, i have a second Iphone 6 giving me the same reminders without the option to opt out of this update which i am highly suspicious of.
As for the comment from Chris above, I would say these large companies like Apple are relying on customers like Chris who obviously do not expect service from there purchases any more, if the phone was working perfectly well before the update why should anyone have to pay for a new phone when the update came from the manufacturer of the phone " take responsibility Apple and replace our phones ! " there are to many cases like this for it to be anything but a partially faulty update with expensive consequences for the customer although on the other side of the coin it creates more revenue for Apple, now thats a whole new senario....."