I have mine working OK now.
It is in fact the 4-pin Molex power connector that's inverted. Normally, you can't get it in the wrong way because two of the corners are filleted to prevent you plugging it in the wrong way. But I found out the hard way: it is very easy to put it in the wrong way. The connector has to go "upside down", so the shaved-off corners are at the bottom, the long flat edge at the top.
As a picture is worth a thousand words and to save more people blowing up their HDDs...