I may post the long story later, but the short story is that I have
a motherboard and a DDR DIMM where pins 3 and 100 on the DIMM and
the corresponding socket are toast. The gold on the DIMM contacts
is completely gone, and the socket is charred in those positions.

The motherboard was said to be dead when the DIMM was installed.

I've taken out the DIMM, and I put another DIMM into the computer
in a different socket, and it seems to work fine.

I took the burned DIMM and put it into another computer, and it
seems to work fine too.

What happened?

(I checked the DDR pinout. Pins 3 and 100 are both grounds.)