On my working Widget, the Power OK pin was pulled up to +5V as James suspected. On my broken Widget, however, this did not happen. There's +5V on the other side of R1, so something else must be pulling it low. There is not much circuit there to do that, though. Pin 2 of U11 is high; pin 3 is low; no surprises there. This result obtains regardless of whether the controller is plugged into the rest of the Widget.
So, I'll need to figure out what's pulling this line low. It gives me hope that this drive can be resurrected---maybe this is the only problem. Happily, I was able to use my UsbWidEx to test the Widget's servo directly: the drive spins up (with much groaning after 20 years of being idle) and the servo walks along the disk in the ordinary way. That's pretty good news, I should think!