The thing about backing up, then restoring from that backup is that you're putting the same image on your device that you have with the problem. It won't solve anything. You need to sync your stuff over that will sync (SMS/MMS will not, address book, mail, pictures, all that fun stuff will), restore and set up as a NEW device, then sync your stuff back over.
Here are the Apple documents to show you how to-
Sync info - iOS: Syncing with iTunes
Restore - iTunes: Backing up, updating, and restoring iOS software
"What, exactly, is the internet? Basically it is a global network exchanging digitized data in such a way that any computer, anywhere, that is equipped with a device called a 'modem', can make a noise like a duck choking on a kazoo." - Dave Barry