OK, here's the back of the board
and here's the front, with the connector plugged in.

As you can see, I connected black/yellow/orange to the GND/TX/RX connectors. I tried swapping the yellow and orange leads, but that had no effect.
I have little to no faith in my ability to solder.
Do you have any recommendations on how to verify that my soldering job is actually connecting to something? I can't think of anything else, since (1) the terminal program and the serial<-->USB connector seem to work when I touch the tx and rx wires in the serial<-->USB connector, (2) I've direct-connected to the Asus via Ethernet, so it works.
Is there anything you can think of that I can do to test this, without redoing the soldering? I suspect that if I have to remove and reattach the connector, I'll burn this last one out too.
Thanks,
Larry