While talking to Dell support, I had to move the power pack so I could read out some codes/numbers on it. Shame, actually, as I’d just got the damned thing working. Of course, after moving it around, I couldn’t get any power to flow again. Next thing you know, while trying to twist the cable around and get things going again, the cable broke entirely.
Whoops…
At least the problem’s no longer intermittent :)