Hi,
The simple answer is: Try again. Maybe a few times.
I don't know why, but sometimes the BF-888S radios don't like to enter programming mode every time. I think this problem affects Windows more than Linux. I've only used CHIRP on Linux.
You are correct that if you can program a UV-5R then you know the cable works. Both the UV-5R and the BF-888S use the same cable and 9600 baud. Even just reading data from the radio requires the computer to transmit serial data to the radio and receive data back from it which proves that all three wires are working.
It doesn't matter which channel the radio is set to. I have just tried all 16 channels and it works on every one of them.
What I did find is that every time you read from the radio, it reboots. Data transfer doesn't work during boot-up, which seems to take around 6 seconds. Because the serial cable is plugged in it is muting the speaker so you can't hear it saying "Power on...".
And before anyone suggests another bit of common superstition, no it doesn't matter what you have the volume level set to.
It is of course possible that they have changed the way the radio works (although for something that cheap and simple, I doubt it), or that the one radio you have has a physical problem with one or both of the connectors.