Why 100nF capacitor between FT232R DTR pin and Atmega reset line is causing problems at boot?
The FT232R and its drivers/firmware are the only important thing for determining the USB device ID, and showing up as something other than Unknown.

It is NOT the reset capacitor from DTR to the ATMEGA328P. 

You either have a dead device, faulty USB cable/connections, you've broken the USB device somehow, or some other shenanigans.

The capacitor from DTR to the ATMEGA is there for the auto-reset feature while programming the ATMEGA and has nothing to do with the process of the FT232R enumerating itself as a virtual COM port. 

The DTR pin is an output of the FT232R, not related to establishing a connection with the PC. It is software controlled in order to pulse the reset line of the AVR during the programming procedure. 

There could be various things wrong as I said before, of why the FT232R is not working properly - I would check for driver issues first. FTDI had in the recent past made a Windows Driver Update which caused counterfeit FTDI chips to become bricked, and you have just encountered this? Either way, try plugging that USB device into other computers which have the FTDI drivers properly installed, to ensure that is not the issue.