I've just run the loopback test and it works correctly (I used Serial Monitor), reflecting all data entered.
I've also just tried the LED test on DO and D1. When uploading, I get a single flash from D0 (and from the onboard Rx0 LED) every 10 seconds, or thereabouts. I get nothing from D1 or the Tx0 LED.
I guess this means the USB chip is playing up? Whilst I don't have an ICSP header adjacent to the USB chip, there are 3 x 2 vias in the board at that spot that I could solder to if that would help, or is there another way to talk to the USB chip?