"I'm powering the board through its Vin pin via an external 5 volt regulated supply. Do you think that might be the cause?"
Yes. Vin needs >= 6.5 to 7V for the onboard 5V regulator to work. Otherwise feeding 5V into the 5V regulator does not result in a workable 5V coming out of the regulator.
If you want to power the board from 5V, connect the source to the 5V pin, or power it via the USB connector.