Thanks for the quick response! So, no additional hardware that I didn't mention, and I can't see anything poking out of the bottom of the Ethernet shield that could be contacting the Arduino main board.
My understanding of the on-board voltage regulator is that it is not used when power is supplied via the USB port?
I do notice that the voltage from the DC charger USB port is slightly higher than from the computer's USB port, but I am having a hard time imagining that things would stop working when the voltage is all the way up to the specified 5V instead of a few tenths of a volt below that. Usually it would be the other way around?
I also tried supplying a regulated +5V from a PC power supply to the Arduino's 5V pin, and that produced the same behaviour as the DC USB charger. I don't think a lack of current or voltage is the problem, as far as I can see.