I will try another 4-pin cable. And I will try a diode between Tx and Rx. It seems to me that the radio is trying to pull down the data line, but the PC Tx line is pulling up (idle).
None of the radios I've built cables for (which is many) have ever had a diode in the mix. The radio expects to see its own echo, so if you try to prevent that with the diode, then it will stop transferring immediately. If you put the diode the other way, then you haven't changed the circuit any.
The PC will float either high or low, but will be pulled either direction. I know it seems strange, but there are lots of devices that do two-way communications on a single wire like this.
I also wonder about using 3.3V. I measured the idle state of the radio's data pin and got about 3V. This made me nervous about using a 5V TTL interface, so I modified the FTDI board to use 3.3V. Many of the interface circuits on the web use 5V (or some hacked power supply from the serial port control lines). Perhaps I should go back to 5V.
Yes, you want 5V. 3.3v at idle could just be where that one floats. Most of these radios are using a very simple and robust driver circuit off of the speaker lines that could probably take the full +/-12V swing without much trouble, so even if you did have a 3.3v unit (seriously doubt it), I bet you'd still not have trouble with 0-5V.