Hello Guys, I truly wish that Apple will solve this problem ASAP. I have too many important messages that I have kept for a long time and will never erase them. Nevertheless, when I upgraded my iPhone today, I had the same problem, which blocks my incoming messages and whenever I open my messages I get the infamous message that says my inbox is full and I have to delete previous messages. Thus I decided to Downgrade my phone to 4.3.5 firmware version. This is for the people who doesn't want to lose any of their messages.
1. Make sure that you have the firmware downloaded and in a location where you could easily find (e.g. Desktop)
2. startup your itunes
3. Conncet your iphone and put it on the DFU mode, here's a link that tells you how:
http://youtu.be/Ufw0vAEEI8M
4. When you see the iphone screen on iTunes, press and HOLD "option" and click on the restore button, then select the firmware file that you wish to downgrade to.
5. When the firmware is downgraded, click on restore from backup (select the last backup OR the backup that you synced your phone to before upgrading).
6. your phone may take a while until it restores fully to the previous version.
All the best my fellow message keepers, and PLEASE APPLE, SOLVE THIS PROBLEM.