The user troubleshooting is power off/on, reset, restore from backup, restore as new. Now you have just downloaded an update to the iOS and that has not resolved the issue. Did the flash ever work? It sounds to me as if you have a hardware issue since this update which restores your phone did not change the issue. I suggest a Genius Bar appointment for a hardware check.
Try restoring as a new phone and see if it works since you've updated already and the phone has rebooted...
If it does, then rebuild your phone wihout restoring from your backup. Something is corrupt in the backup.
If that doesn't fix it, make an appointment at the genius bar and take it in for service.