I have the same issue with an arduino nano project wich is powered by a battery. The USB is not working when the nano board is powered by the baterry. When I unplug the Nano board the USB is working fine. I don't think that the nano has smoked. If the FTDI is smoked it shouldn't work in any case.
At the start of this project I have use an arduino Uno board. All is working just fine with the same parts that don't work with the Nano board. I think that the FTDI component should be powered by the USB. It should solve this issue..