Unable to sync apps on new iPhone 5

Question

Brand new iPhone 5.
Old iPhone 3GS backed up with iTunes.
iTunes updated to 11.0.1.12 and backup restored to new iPhone. Music, messages etc all synced. Apps do not sync despite many attempts.
iTunes Apps page is checked for "Automatically sync new apps"
iPhone Settings > General > Restrictions not enabled.
iPhone is logged into App Store and so is iTunes.
iTunes has a strange phenomenon. When turned on and conneced to the phone, there are only four screens:
Now, if I begin to drag some apps from the left, this is what happens:
Notice the extra screens that appeared on the right  They were created some time ago after the purchase by dragging every desired app.
Clicking Apply goes through the motions of a sync very quickly, but nothing is transferred to the iPhone 5.
The buttons on the bottom right change to say "Sync"
If I click "Sync", very briefly, the progress bar (or whatever it is called) shows the green Apps bar a little wider, but then it shrinks back to the slim green bar.
No app has synced and the phone still has three screens, not what iTunes shows.
Please advise.
Added diagnostics report:
Microsoft Windows 7 x64 Home Premium Edition Service Pack 1 (Build 7601)
HP-Pavilion NY758AA-ABG 300-1040a
iTunes 11.0.1.12
QuickTime 7.7.3
FairPlay 2.2.32
Apple Application Support 2.3.2
iPod Updater Library 10.0d2
CD Driver 2.2.3.0
CD Driver DLL 2.1.3.1
Apple Mobile Device 6.0.1.3
Apple Mobile Device Driver 1.63.0.0
Bonjour 3.0.0.10 (333.10)
Gracenote SDK 1.9.6.502
Gracenote MusicID 1.9.6.115
Gracenote Submit 1.9.6.143
Gracenote DSP 1.9.6.45
iTunes Serial Number xx
Current user is an administrator.
The current local date and time is 2012-12-28 13:40:21.
iTunes is not running in safe mode.
WebKit accelerated compositing is enabled.
HDCP is supported.
Core Media is supported.
Video Display Information
ATI Technologies Inc., ATI Radeon HD 3200 Graphics 
**** External Plug-ins Information ****
No external plug-ins installed.
Genius ID: xx
**** Network Connectivity Tests ****
Network Adapter Information
Adapter Name:          {xx}
Description:          802.11n Wireless LAN Card
IP Address:          192.168.0.18
Subnet Mask:          255.255.255.0
Default Gateway:          192.168.0.1
DHCP Enabled:          Yes
DHCP Server:          192.168.0.1
Lease Obtained:          Fri Dec 28 11:40:30 2012
Lease Expires:          Sat Dec 29 11:40:30 2012
DNS Servers:          192.168.0.1
Adapter Name:          {xx}
Description:          Realtek PCIe GBE Family Controller
IP Address:          0.0.0.0
Subnet Mask:          0.0.0.0
Default Gateway:          0.0.0.0
DHCP Enabled:          Yes
DHCP Server:
Lease Obtained:          Thu Jan 01 11:00:00 1970
Lease Expires:          Thu Jan 01 11:00:00 1970
DNS Servers:
Active Connection:          LAN Connection
Connected:          Yes
Online:                    Yes
Using Modem:          No
Using LAN:          Yes
Using Proxy:          No
Firewall Information
Windows Firewall is on.
iTunes is NOT enabled in Windows Firewall.
Connection attempt to Apple web site was successful.
Connection attempt to browsing iTunes Store was successful.
Connection attempt to purchasing from iTunes Store was successful.
Connection attempt to iPhone activation server was successful.
Connection attempt to firmware update server was successful.
Connection attempt to Gracenote server was successful.
Last successful iTunes Store access was 2012-12-28 13:36:52.
**** CD/DVD Drive Tests ****
No drivers in LowerFilters.
UpperFilters: GEARAspiWDM (2.2.3.0),
E: hp DVD A  DL8ATL, Rev PH1F
Drive is empty.
Error Correction is turned on for importing audio CDs.
**** Device Connectivity Tests ****
iPodService 11.0.1.12 (x64) is currently running.
iTunesHelper 11.0.1.12 is currently running.
Apple Mobile Device service 3.3.0.0 is currently running.
Universal Serial Bus Controllers:
Standard Enhanced PCI to USB Host Controller.  Device is working properly.
Standard OpenHCD USB Host Controller.  Device is working properly.
Standard OpenHCD USB Host Controller.  Device is working properly.
Standard OpenHCD USB Host Controller.  Device is working properly.
No FireWire (IEEE 1394) Host Controller found.
Connected Device Information:
Kate’s iPhone5, iPhone 5 (CDMA) running firmware version 6.0.2
Serial Number:          xx
**** Device Sync Tests ****
Sync tests completed successfully.
Message was edited by: crm911

Answer 1

Dfu means device firmware upgrade
Press and hold Power + Home buttons together (10sec)
Phone will go blank
Before Apple logo comes, release the Power n keep holding Home button
Until you see a pop in the PC that Apple device in recovery mode
At that point iTunes will pop asking to restore iphone
Click restore or
before u click restore just download the iOS 6.0.2 on say desktop
After that press and hold shift on ur keyboard then click restore
It will allow u to navigate and select the iOS firmware u just downloaded
That's it. When done, restore from your iphone backup, and syncing starts working