How to Fix iOS Upgrade Issues
For those who are having problems. I have been an iPhone beta tester and I am a developer as well. We run into tons of problems doing over-the-air updates in the iOS 7 beta tests. The problem has to do with certain database files that get corrupted in the iOS system directories. These databases contain, among other things, information about your iCloud account credentials and certificates used to validate your device to the servers. When the DB gets corrupted, it can cause issues with these services. We saw a lot of issues with iMessage for example.
Here is a method that I found works well to resolve issues.
Before you start, make sure you have at least as much free HDD space on your computer as your iPhone's capacity. Ideally more. If you don't, and you're on Mac, then use the nifty app WhatSize on your Mac to find big files on your computer and delete them to free up space.
STEP 1: back up any existing versions of important apps that are in your iTunes folder on your computer in /Users/You/Documents/iTunes/Mobile Applications/. (Time Machine already does this, so if you're using that, then you should be fine, but I burn them off to Panasonic 50-year Archival Blu-Rays to protect them from ever getting purged as old data from my Time Machine drive. That way if a developer updates an app and it sucks, I can downgrade back to a previous version of that app.)
OPTIONAL STEP: If you have a lot of photos and movies taking up space on your phone, I recommend that you download all the contents of your Camera Roll (photos and movies) to your computer, then create a second back up to Time Machine or an external drive, then delete them off of your phone. This will greatly speed up the backup/restore process (in the next steps).
OPTIONAL STEP: If you have lots of big recorded data files in other apps, such as Garage Band recordings, etc., it will also speed up the backup/restore process to transfer them off of your device to your computer using iTunes file sharing or a third-party utility like PhoneView/iFunBox that lets you copy files in and out of application-specific directories on the iOS file system. (You can always put this data back later.)
STEP 2: Connect the iPhone to your computer and launch iTunes. Right-click the device and select "Transfer Purchases". Let that finish up. It can take awhile, especially if you've never done it before.
STEP 3: Click "Back Up Now" under "Manually Back Ups and Restore" to create a full, current backup of your iPhone to iTunes on your computer. (If you don't do this on a regular basis, now is the best time to start!) This takes a fair amount of time. It may take a really really long time if you have not done the OPTIONAL STEP(s) above and your iPhone has lots of data on it.
STEP 4: Back up your latest back up, iOS apps, photos, etc. If you use Mac and have a Time Machine drive, then do "Back Up Now" from the Time Machine menu and wait until it completes. (That way if your HDD fails during the next step, you won't lose all the data from your phone.) If you don't use Time Machine and/or Mac, then find an alternate way to back up your iTunes backups. The easiest way is to simply copy the /Users/You/Library/Application Support/MobileSync/Backup/ directory to an external volume (USB stick, hard drive) or burn it to Blu-Ray (this is the ideal solution since BD-R can last 50 years even through a major solar flare). (If you use iCloud Backup from your phone, this can also serve as a secondary backup, but I do not trust clouds. Clouds can evaporate.)
STEP 5: Click "Restore iPhone..." and proceed. This will erase your iPhone and rebuild all databases, restoring everything to factory defaults.
STEP 6: Set up your iPhone as a New iPhone. Enter your iCloud information and get yourself to the point where iMessage is working, phone is working, text messages are working. If they still aren't working then you have a hardware problem with your phone: take it to Apple. But 99% chance these services will be working fine. Test it with your e-mail servers too if that was causing you some problems, just make sure to set up with IMAP and don't delete things of your e-mail servers.
STEP 7: Now, click "Restore Backup..." and restore the previous backup you made in STEP 3. This will start from the newly-rebuilt databases and import your settings from the previous backup. This takes awhile.
STEP 8: Your phone should be working now. Use it. Don't forget to make regular back-ups!