This took longer than I expected because the problem was more complex than I thought. I was getting strange results partly because my Windows system was unstable. I ended up having to do a fresh install before I could proceed.
I'm now working with a different adapter (a GeForce 8800 Ultra), but I have the same problem with it, so I think we can proceed from where we were.
When I had a stable system again I found that nvidia-smi (NVIDIA's command line utility roughly equivalent to CPU-Z) reported that it could not get information from the card. This appears to be a driver problem, although the driver seems to be working perfectly in other respects. The Linux version of nvidia-smi has no such trouble. I suspect that whatever is upsetting the Windows version of nvidia-smi is also causing CPU-Z to report 0 MB of RAM. If anyone can confirm this and/or suggest a fix, I'll be grateful.
I've uploaded a GPU-Z screen shot (see next message), and I have a couple of text captures from nvidia-smi, which I'll copy below.
nvidia-smi from Windows:
C:...>"C:\Program Files\NVIDIA Corporation\NVSMI\nvidia-smi"
NVIDIA-SMI has failed because you are not:
a) running as an administrator or
b) there is not at least one TCC device in the system
(Yes, I am running as administrator. This is an experimental system, and the only account I've defined on it is an administrator account.)
nvidia-smi from Linux:
Tue Apr 11 01:43:28 2017
+------------------------------------------------------+
| NVIDIA-SMI 340.102 Driver Version: 340.102 |
|-------------------------------+----------------------+----------------------+
| GPU Name Persistence-M| Bus-Id Disp.A | Volatile Uncorr. ECC |
| Fan Temp Perf Pwr:Usage/Cap| Memory-Usage | GPU-Util Compute M. |
|===============================+======================+======================|
| 0 GeForce 8800 Ultra Off | 0000:01:00.0 N/A | N/A |
| 60% 56C P0 N/A / N/A | 197MiB / 767MiB | N/A Default |
+-------------------------------+----------------------+----------------------+
+-----------------------------------------------------------------------------+
| Compute processes: GPU Memory |
| GPU PID Process name Usage |
|=============================================================================|
| 0 Not Supported |
+-----------------------------------------------------------------------------+