Try to force the install of the attached drivers on your "bricked" FTDI arduino.
They are just a modified version to work with FTDI chips que have the PID changed to 0
Thanks for the information, but when I install the driver, I have Windows 7, I have the USB Serial Converter, but when I look to the properties, I have : "Windows can not verify the digital signature of the required drivers for this device. It is possible that a recent hardware or software change has installed a damaged or whose signature file is incorrect, or whether it is malicious software from an unknown source. (Code 52)" (translation from French), and impossible to have a COM Port for the RX board.
I have also seen on internet, that there can be a problem with the Arduino Nano and the FTDI chip. Usually it works but sometimes, particularly when an external power input is used, the FTDI chip inside the Arduino does not want to be detected by computer, if the pin 26 (TEST) of the FTDI Chip is not connected to ground, this is a bug made by the developers of Arduino. The solution is to make a bridge between pin 26 and 25 (AGND) by soldering them together. But for the moment I am waiting for the header female connectors, so I can desolder the Nano board.