Well! File this one under "problem solved".
After waiting around most of a week for Melrose Mac to order a brand new card and install it, it turns out that the problem is actually this:
Sonnet cards must be installed in Slot 3 or 4. They cannot be installed in Slot 2.
So, the original card that they replaced was undoubtedly in fine working order. They just didn't know what they were doing when they installed it.
After a single post on the Apple Support Discussions thread, I had the answer within a couple of hours.
What really bothers me is that when I picked my computer up, today, the service technician assured me that they had, in fact, turned my computer on and checked that the new card was now working. I mean, it's one thing to be incompetent, and another to lie to your customer's face.
Anyhoo ...