(It is at this point that it occurs to me that perhaps if I had not already been convinced that the problem with the adapter was the malfunctioning USB ports on the old mobo, I might have tried this a couple of weeks ago and saved myself a lot of time and money. OTOH, it was a seven-year-old computer, and now I have a much faster machine .)
So now it's time to connect the old hard drive and see if I can read it. Which I do, and I can. I think. There might be a missing partition there, but I can definitely read my old files. I still have to reinstall Office, but I've got antivirus software and all the Windows patches taken care of. Though now the monitor is being a bit flaky, and I still have the nonbooting optical drive to deal with...maybe next month. I've kind of blown the discretionary budget for a while.
How much faster? Before removing the old mobo, I backed up FireFox and Thunderbird email using MozBackup to extract the profiles. It took a while to do Thunderbird, as I have a lot of saved emails--a few Gb worth. I had reinstalled FireFox and Thunderbird, reloaded the default profile (including user history, bookmarks, plugins, etc.) for FireFox (it took a few seconds), and then when I reloaded the email profile it also took a few seconds. I was not expecting that, after how long it took to save the profile, so I checked to make sure that it had, indeed, put in all the emails. It had. In about a tenth or less of the time it took to save them. Whee!