I am having nearly this identical problem, only with Windows 7. Have you been able to find a solution?
I purchased 4 Arduino Due R3-E boards from Mouser, and the driver is not found for any of them. I've tried Arduino IDE 1.5.5, 1.5.8, and 1.6.0, all to no avail. I have 2 Arduino Due R3 boards (not R3-E) purchased about a year ago, and they work fine. (So it isn't the cable, computer, or user error.) We have tried no less than 4 different machines.
If other people are having this same problem, I wonder if this could be a bad batch somehow?
OK, I think I've got this figured out. I was able to use the Linux version of the Arduino 1.6.0 IDE to upload a sketch to my stubborn Due, which showed the problem isn't the Due hardware. I went back into Windows to try and "force feed" it the driver, and it worked. Here is the procedure I followed:
Device Manager, right click on the "Arduino Due Prog. Port"
-> Update Driver Software
-> Browse My Computer for Driver Software
-> Let me pick from a list of devices
The Arduino Due might show up in the list if you are patient enough to wait for it to load and you already have the driver installed. I clicked on "Have Disk" then navigated to the .inf file in the Arduino drivers folder. From there I was able to select the correct driver ("arduino Due Prog. Port"). This worked for me on Windows 7, your mileage may vary.