Arduino Due not working properly

Hi,

I was working normally with an Arduino Due R3 board (Arduino IDE 1.5.8 BETA, Windows 8.1) when suddenly it stopped working. When I connect the board to the PC using the Programming Port, both "ON" and "L" LEDs turn on, but when I try to upload the sketch, the IDE displays the message: "No device found on COM3". When I use the Native Port, both LEDs turn on too, but Windows can't even recognize the device, so I can't select the COM Port in the "Tools" section.

I tried to press "RESET" and "ERASE" buttons, using both ports, and nothing happened. I also tried to upgrade the 16U2 firmware using an Arduino UNO as an ISP and it didn't work. I noticed that when I press the "RESET" button, "L" LED doesn't blink, but the troubleshooting page (http://arduino.cc/en/guide/troubleshooting) says it was supposed to blink because of the bootloader, so there could be a problem with the bootloader. However, I read that the SAM3X8E comes with a built-in bootloader permanently burned in the chip ROM, so maybe this is not the problem.

Does anyone know what could be happening? I am totally lost here and I really appreciate any help you can provide!