Hello GWN,
nvstor32 is indeed a SATA driver. Prior to some time last week, the NVidia website had a 'Motherboard' button on its driver download page which, presumably, took us to a page full of motherboard drivers to download. Unfortunately, that button didn't work properly and I couldn't get any further, nor could I find a download elsewhere (at least, not one I'd be confident was the real thing). Suddenly, that 'Motherboard' button has disappeared and all their drivers are now available directly from the downloads page. As a result, I've been able to install a new nvstor32.sys. I guess now I have to wait and see if the BSOD happens again.
As for the graphics card, I did install a new one a few years ago after the previous one started failing, and that would have been after 2012. The GeForce 7300 update will be a remnant of the previous card.
The GeForce Experience software is something that came with the new graphics card, and I never thought to remove it from start up. I don't use it (apart from checking for driver updates) and it doesn't need to be running all the time, so I've just disabled the service that launches it.
I've been reluctant to run the hardware diagnostic that bwv848 suggested, partly because I wanted to update nvstor32 first, but mostly because the BSOD itself isn't really a problem for me. It's very intermittent and only happens on start up, so I never lose anything and all I have to do is reboot and everything's OK. Investigating the BSOD is really just a means to an end, the end being to get the missing Windows updates installed. If the BSOD turns out to be a hardware problem - and given the age of the PC and the fact the BSOD only ever happens on start up, I would guess hardware is the most likely cause - then I'd be happy not to take up any more of his time, because I can't see how an intermittent hardware fault could be causing the failure to install any Windows updates (unless you can convince me otherwise!), and there are people out there with more troublesome BSODs than me.
So, the plan now is to wait and see if I get another BSOD with this new nvstor32 installed. I'll give it a few weeks (unless one happens earlier). In the meantime, is there anything else you could suggest regarding the Windows updates?
Thanks