Hmm. Scrap one theory. I have checked the individual contacts in the socket - all of them are nice tight fits on the end of a paperclip, just like the ones I tested on the scrap motherboards.

And it looks as if the flipping socket on the card is designed to fit into the metal mounting bar, so a socket off a motherboard won't do.

Time to take card off motherboard again and check for continuity between pins and solder tags.