This has happened to me twice. The first time, I got a replacement from Verizon.
The second time, I refused to deal with being without a phone for 3 days as it is necessary for my work.
Mine had gotten to where it would not even try to turn on without the charger, and even then never got past the boot up screen. I left it on the charger and pulled the battery. Let the phone go off again, then disconnected the charger and removed the SD card. Next, plug the charger back in and attempt to boot the phone. It shouldn't get too far without coming up with an error about not having an SD card in the phone. After this, I put the SD card and battery back in, and booted it up without the charger.
I actually just lost all of my contacts, about 14 hours after I installed the update. As I freaked out and started trying to import contacts from the SD card (to no avail) and rebooting the phone, I finally just let it sit because I was too busy with work to keep messing with it. About 15 minutes later, it was perfectly fine and reloaded everything.
This got mine back up and running, without losing any apps or contacts. Hope it works for you.
-Jeff