Microsoft Update searches for updates but never completes

On my computer, when I visit the Microsoft Update site, it always first
checks to see if the ActiveX control is installed. And then when I tell it I
want a Custom update (rather than Express), it sits there forever, with the
green progress bar going back and forth.

I've since installed Windows Defender, and when I ask it to check for new
definitions, it says it is (I get a ballon tip in the status bar). But again
this never completes.

I thought this might have something to do with Zone Alarm being installed,
so I uninstalled it (replacing it with AVG Free).

The only other clue I have is that if I try to stop the Automatic Updates
service, this action too never complets.

If I look in the history, the machine has successfully installed updates in
the past (before I purchased it, second hand).

But now, the Microsoft Update site, Windows Defender and the automatic
Windows Upate service are all not working for me.

Any pointers gratefully received. Attempting to Google an answer has so far
got me nowhere :-(
.