Follow these steps to temporarily disable Driver Signature Enforcement:
http://arduino.cc/forum/index.php/topic,94651.msg727588.html#msg727588

Take note of the Secure Boot step if this is a new system with Win8 installed.

Take a look at this thread:
http://arduino.cc/forum/index.php/topic,140068.msg1057451.html#msg1057451

Maybe your ASUS is having a similar problem to Acer.

It's possible it's related to Secure Boot. There may be a setting in the BIOS setup screens to disable Secure Boot.
I would try disabling Secure Boot, if it is enabled, then try the steps you did before to disable Driver Signature Enforcement.

On mine I have pages of topics listed. And I don't use Notify very often. The vast majority are topics that I have replied to.

Seems like something with your profile settings on the server is messed up.

Is there something unique about this Windows 7 install that you haven't mentioned?
Is this a "corporate" image or something like that, with a group policy set to restrict unsigned drivers?

A standard install of Win7 x64 does not have this issue, other than the warning during the first install.
I use it on Win7 x64 all the time without the problem you describe.

The problem you describe, seems to indicate there is a policy setting that is enforcing this behavior.

Go to your Profile -> Notifications and Emails and then unsubscribe from the thread you no longer want.

Since the Device Manager is showing "atmega16u2", your Arduino is in DFU mode.
This indicates the atmega16u2 does not have the Serial to USB code loaded on it.

If you want to try to recover it yourself you can use the following page as a guide.
http://arduino.cc/en/Hacking/DFUProgramming8U2

The instructions are the same for the 16u2.
Since you are on Windows, you can download and install FLIP. (The link is on the page above)

Download the following firmware and install this on the 16u2 with FLIP:
https://github.com/arduino/Arduino/blob/master/hardware/arduino/firmwares/atmegaxxu2/arduino-usbserial/Arduino-usbserial-atmega16u2-Uno-Rev3.hex

After that, you should be able to install the UNO USB serial drivers.

Hopefully, the bootloader is installed on the atmega328.

Then follow these steps to install the Arduino drivers:

Right click the Unknown Device in Device Manager
Select Update Driver Software
Select Browse my computer for software
Click Browse button
Select the Drivers folder under the location of your Arduino software installation. (Do not select the FTDI folder inside the Drivers folder)
Click OK
Click Next

Just FYI...

When you disable driver signature enforcement, it is only temporary. It disables enforcement for only one session. After a reboot, it goes back to signature enforcement.

Follow the steps here to disable driver signature enforcement on Win8:
http://arduino.cc/forum/index.php/topic,94651.msg727588.html#msg727588

Then follow these steps to install the Arduino drivers:

Right click the Unknown Device in Device Manager
Select Update Driver Software
Select Browse my computer for software
Click Browse button
Select the Drivers folder under the location of your Arduino software installation. (Do not select the FTDI folder inside the Drivers folder)
Click OK
Click Next

Look for the setupapi.dev.log file in your Windows folder.

Open with a text editor and go toward the end of the file. The last sections should indicate what errors are encountered during the .inf installation.

You should see a section that begins with something similar to this:
>>>  [Device Install (Hardware initiated) - USB\...

This error can also be caused by a corrupt preferences.txt file.
Delete this file and relaunch the IDE to see if it clears it up.
See here for info to help you locate the file:
http://arduino.cc/en/Hacking/Preferences

Here is some helpful information about using libraries:
http://arduino.cc/en/Guide/Libraries

I don't think that all components of the Windows version of the IDE are 64 bit compatible.
The only way that I could get the IDE to work with an external version of Java on Win 64 is to install the 32 bit version of Java.

[Drivers]

It's not clear from your post if you have followed these steps to install the com port drivers:

Right click the "Arduino Due Programming Port" in Device Manager
Select Update Driver Software
Select Browse my computer for software
Click Browse button
Select the Drivers folder under the location of your Arduino software installation. (Do not select the FTDI folder inside the Drivers folder)
Click OK
Click Next

See this commit:
https://github.com/arduino/Arduino/commit/85bf4252f0bfaf7fb86111c2104eb089c3a67496

They updated avr_tools.zip with the 5.11 version of avrdude.