Thanks for the response.
I was at 10.5.8 when the problem first appeared.
Later I upgraded to 10.6 then 10.7 for unrelated reasons. When I realized that I preferred 10.5 I erased the disk and reinstalled 10.5.
I included this bit of history only to illustrate that the reinstall of 10.5 did not correct the problem.
I am now at version 10.5.8.
I'll try to explain the problem better.
From observation it seems that each application has a certain amount of Help information stored locally. If none of that Help applies to the terms entered in the Search field then it appears that the application attempts to find the answer to those terms over the internet. I see this in all OS X apps as well as Firefox. The only other application I have is Quicken 07 and it does not appear to try to use an online search for Help.
In my current case the above scenario results in "Searching..." endlessly with no results. It is what I might expect if I had lost internet connectivity, but that is not the case. It seems as though the application and/or OS X has "forgotten" how to find its desired souce of data online.
For what it's worth, as far as I can tell Spotlight and all other Help functions are working as I think they should.
I hope this clarifies the problem and doesn't muddy it further.
Try running your Leopard install disk again, as well as the 10.5.8 combo updater. This might reinstall any 'missing bits'.
You can do this without deleting the hard drive, just install straight over your existing system, but close all applications and external devices first.
Or you could also do this via an Archive and Instal:
How to Archive & Install:
and this also:
This document explains how to correctly reinstall a prior version of Mac OS X in the event that other troubleshooting does not resolve an issue:
BUT: Don't install older versions of Mac OS than what came with your computer: