Even though I have a 64 bit version of iTunes, whenever I connect my iPhone it asks me to install 64 bit version of iTunes

Question

I reinstalled itunes 10.5.3 64 bit version on my Windows 7. When I connect my iPhone it gives me a error message of incorrect version and to uninstall and reinstall with 64 bit version. I have tried this over and over again but this message is not going. 
I am not able to connect my iPhones 3GS (32GB) with my laptop. Please help!
I am sending the result of the diagnostics
  Microsoft Windows 7 x64 Home Premium Edition Service Pack 1 (Build 7601)
ASUSTeK Computer Inc. NX90Jq
iTunes 10.5.3.3
QuickTime 7.7
FairPlay 1.13.37
Apple Application Support 2.1.6
iPod Updater Library 10.0d2
CD Driver 2.2.0.1
CD Driver DLL 2.1.1.1
Apple Mobile Device Driver 1.57.0.0
Bonjour 3.0.0.10 (333.10)
Gracenote SDK 1.9.5.502
Gracenote MusicID 1.9.5.115
Gracenote Submit 1.9.5.143
Gracenote DSP 1.9.5.45
iTunes Serial Number 0041AD5C0337DA28
Current user is not an administrator.
The current local date and time is 2012-03-05 16:27:34.
iTunes is not running in safe mode.
WebKit accelerated compositing is enabled.
HDCP is supported.
Core Media is supported.
Video Display Information
NVIDIA, NVIDIA GeForce GT 335M
**** External Plug-ins Information ****
No external plug-ins installed.
**** Device Connectivity Tests ****
iPodService 10.5.3.3 (x64) is currently running.
iTunesHelper 10.5.3.3 is currently running.
Apple Mobile Device service 3.3.0.0 is currently running.
Universal Serial Bus Controllers:
Renesas Electronics USB 3.0 Host Controller. Device is working properly.
Intel(R) 5 Series/3400 Series Chipset Family USB Enhanced Host Controller - 3B34. Device is working properly.
Intel(R) 5 Series/3400 Series Chipset Family USB Enhanced Host Controller - 3B3C. Device is working properly.
No FireWire (IEEE 1394) Host Controller found.
Most Recent Devices Not Currently Connected:
iPod touch running firmware version 3.1.3
Serial Number: 9C8113AB14P
iPhone 3GS running firmware version 5.0.1
Serial Number: 870031DL3NR
**** Device Sync Tests ****
No iPod, iPhone, or iPad found.
The exact error message is
This iPhone cannot be used because the required software is not installed. Run the the iTunes installer to remove iTunes, then install the 64 bit version of iTunes.

Answer 1

This iPhone cannot be used because the required software is not installed. Run the the iTunes installer to remove iTunes, then install the 64 bit version of iTunes.
That usually indicates that your Apple Mobile Device Support has not installed. That's also what is being shown by the diagnostics (the driver is there but the application isn't).
Let's try a standalone Apple Mobile Device Support install. It still might not install, but fingers crossed any error messages will give us a better idea of the underlying cause of why it's not installing under normal conditions.
Download and save a copy of the iTunesSetup.exe (or iTunes64setup.exe) installer file to your hard drive:
http://www.apple.com/itunes/download/
Download and install the free trial version of WinRAR:
http://www.rarlab.com/
Right-click the iTunesSetup.exe (or iTunes64setup.exe), and select "Extract to iTunesSetup" (or "Extract to iTunes64Setup"). WinRAR will expand the contents of the file into a folder called "iTunesSetup" (or "iTunes64Setup").
Go into the folder and doubleclick the AppleMobileDeviceSupport.msi (or AppleMobileDeviceSupport64.msi) to do a standalone AMDS install.
(If it offers you the choice to remove or repair, choose "Remove", and if the uninstall goes through successfully, see if you can reinstall by doubleclicking the AppleMobileDeviceSupport.msi again.)
Does it install (or uninstall and then reinstall) properly for you?
If instead you get an error message during the install (or uninstall), let us know what it says. (Precise text, please.)