Well, I took some time to look at the power supply. Turns out it is indeed the power supply that has failed. There are roughly 1V differences in voltage over a period of about 1 second.
This is what I saw on my scope. I was measuring the power input to the SheevaPlug motherboard, which I suspect is supposed to be somewhere around +5V -- the transients seem to push this to about +7V. Whoops. Explains the LED behaviour, I suppose (interestingly, the transients I'm seeing occur at the same frequency as the LED is blinking). Notice that this is over a 2 second period.
Time to email Globalscale Technologies support, I suppose.
EDIT: fixed typo.