My phone has turned into Lionel Richie - it keeps saying "Hello"

Question

I jest, only because if I don't laugh I will cry.
I've been holding off on updating to 7.1 because I knew there were problems with it.
Earlier today my phone wouldn't connect. iTunes insisted I update, so I did. To 7.1.1 I believe.
Now it refuses to leave the "Hello" setup screen. I've restored four times in DFU. I've updated iTunes and restored again.
To add insult to injury it says I have three backups from today (of the empty phone) and two from 2012!!
2012!
This is the phone I've been backing up to my macbook pro every two or three days. I've found one legit looking backup in the library with seems to be about the right size and is from this morning before I updated, but it doesn't appear in the backup list. I have downloaded the Reincubate iphonebackupextractor and it can see stuff in the one existing backup that looks ok.
Besides, even if it did I would back up to it and the fricken phone would go all Lionel Richie again. It says it's syncing and takes ages, I can SEE the apps (sans data I assume)  but I can't get the phone to stop saying "Hola".
I have always defended Apple's prices on the basis that you plug them in and they work. Steve Jobs must be spinning in his grave.
I have read all the fixes here and online and tried them. They don't work for me. I believe there is hope but at the moment I don't have a phone. My work phone. The one people use to ring me for work.
Help! (I know that's the Beatles but it's supremely relevant here.)

Answer 1

Since the iTunes restore is putting your iPhone back to the start of the set up process, I would try to avoid setting it up from the iTunes backup.  If you set it up as new, it will only have the native Apps and none on your data, but if you have your data on iCloud, not as a backup, but as a sync I would suggest you go that route as something in the backups you have used before might be the reason why you cannot successfully complete the restore.
So I suggest you complete the set up as a new iPhone, then go to Settings > iCloud and sign in with your Apple ID and password and toggle on all the items where you have your info synced to iCloud like contacts, calendar, notes, etc.  If you are unsure of what you have there, you can use your computer to go to iCloud.com and see exactly what you have in each of the icons that would get synced to your iPhone.
If this works, I would try to avoid restoring from the backups.