After much trial and error, a user on the microsoft.public.windowsupdate newsgroup (Bob Anderson) has posted a fix for those of us suffering the "Windows hangs when I try to access Microsoft Update" problem.

Turns out that there is some incompatibility between the nVidia IDE driver (not really used by my system anyway) and the Windows Genuine Advantage validation tool required by Microsoft Update.

So: All you have to do is go to "Add or Remove Programs", select "nVidia Drivers", and tell it to remove just the IDE driver. You will have to reboot, and after that, it all works perfectly.

Who'da thunk it? All's well that ends well, anyway.