So, here I am swapping the IDE card in my desktop in an attempt to make IDE work. Now, being an IDE card it wants drivers. So I very carefully went to the Promise website to make sure I had the latest drivers, and very carefully checked just which files I needed, and very carefully unpacked them to a sensible location under E:\. Then I shutdown the computer, installed the card, and brought it back up.
Guess which physical drive E: resides on? Guess which physical drive is connected through the IDE card I just swapped?
There was a wonderful "wait a minute..." moment when I realised that. On the plus side, my choice of "Safe Mode with Networking" turned out to be the correct one.