Thanks for that advice. It worked - partly!  The run of the downloaded exe
further downloaded "Windows Desktop Update" and installed it.  After
manually rebooting - the software didn't demand it - I had v 4.72.3612.1700
of shell32.dll installed.

However there was a glitch with the reboot, a message "an error occurred
calling DLLINSTALL in C:\Windows\System\shdocvw.dll" (HRESULT=80004005).
Booting completed, but I found two main problems with the result.  First,
the windows had changed to the kind where each new window hides the previous
one, and I couldn't get them changed back with View/Folder Options, which
told me "operation cancelled due to restrictions in effect on this
computer".  Second, my Start menu was empty.

But I was able to establish that the application problems which I hoped the
update of shell32.dll would cure weren't cured by it - complaining messages
about old versions of shell32.dll disappeared, but the problems still
happened.  So that is progress, and I am back with version 4.00.1111 of
shell32.dll again now!

Thanks for giving me the information to enable me to try this out,
Ciarán Ó Duibhín.

Create a backup of your current configuration, then download
http://www.download.windowsupdate.com/msdownload/update/v3/static/ie501sp2/x
86/en/ie5setup.exe
Start Notepad, copy and paste the following text to it and
save it as "iebatch.txt" to the same folder as the "ie5setup.exe"
file.  Then double-click the "ie5setup.exe" file.  A reboot will
be required.

[DownloadSite]
Display=0
DownloadLocation="http://www.download.windowsupdate.com/msdownload/update/v3
/static/ie501sp2/x86/en"
[Custom]
SetupMode=0
Component=IE4Shell_Win
[Options]
Quiet=U
[Reboot]
Reboot=0
[End]

Ben