Arduino uno on Windows 7 32 bit, that device cannot start ( code 10)

Here is the relevant section from the log on my system.

Notice the first line from my log snippet:
[Device Install (DiShowUpdateDevice) - USB\VID_2341&PID_0001\64932343738351410122]

This is the device that it is installing the drivers for. It is a USB device with the Arduino UNO VID/PID

In your logs it shows your are trying to install the drivers for:
[Device Install (DiInstallDevice) - ROOT\PORTS\0000]

This does not seem correct.

What device shows up in Device Manager when you have the Arduino connected to the system? Can you attach a screen shot of the Device Manager with it connected?

[Device Install (DiShowUpdateDevice) - USB\VID_2341&PID_0001\64932343738351410122]
>>>  Section start 2012/09/08 11:07:08.253
      cmd: "C:\Windows\system32\mmc.exe" "C:\Windows\system32\compmgmt.msc" /s
     dvi: {DIF_UPDATEDRIVER_UI} 11:07:08.268
     dvi:      No class installer for 'Arduino Uno'
     dvi:      Default installer: Enter 11:07:08.268
     dvi:      Default installer: Exit
     
     ...

     ndv: {Update Driver Software Wizard exit(00000000)}
<<<  Section end 2012/09/08 11:08:03.137
<<<  [Exit status: SUCCESS]