I would appreciate some help:

When I right-click on any of the icons on the Quick Launch Toolbar, I get the usual menu:
Open
Explore
PFrank
Search
WinMerge
Geosetter
Scan with AVG
Send to
Cut
Copy
Create Shortcut
Delete
Rename
Properties

Left-Clicking on any of these options works as it is supposed to.

However, if I right-click on any of the QL Toobar icons a second time, the Taskbar menu appears, preceded by
Open folder (this opens the Quick Launch Toolbar folder)
Toolbars
Cascade Windows
Tile Windows Horizontally
Tile Windows Vertically
Show the Desktop
Task Manager
Lock the Taskbar
Properties

and, crucially, left-clicking on any of the icons has no effect.
(Broadly speaking, the same happens with the Desktop toolbar.)

I have already established, with the help of Katana on http://forums.spybot.info/showthread.php?t=29717 that I do not have any malware. You can see that thread to look at the various logs produced.

At her suggestion, I used http://www.kellys-korner-xp.com/taskbarplus!.htm - the Taskbar / "Toolbars greyed out or missing" option restores icons' left click function by restarting the Windows Shell.

I am running Windows XP Professional SP3 (but another laptop on the network running SP2 has the same problem.)

You have 2 computers doing the same thing? Very odd. The fixes you said you have done, did you do them on both. Have you recently added something to both systems?

I ran Kelly's-Corner-XP TaskbarPlus! on both computers today, but other than that I have only run ComboFix on my laptop - my wife uses the other.

Recently we have both upgraded to Mozilla Firefox 3, AVG 8, and installed Geosetter. We have also begun using a Vodafone USB Modem for our Net connection, using its own VCMLite software.

When the problem first arose we had both received, and opened, emails from someone whose computer had been hit by a virus, so we assumed it had infected us too, but Katana found no evidence of this. There's a Combofix log in the parallel thread

I read your other post. You understand that this is an active and opened post? I realize no one has answered yet, they are extremely busy, but you should not make any changes unless instructed to from a HJT team member. You can post HERE about not getting an answer in 5 days