I will remove the 9200 PCI ATI graphics card and install the NVIDIA GeForce 6200 AGP card. After ten minutes, I know the graphics card will cause the window manger, of the currently running application, and cursor to freeze. If possible, I will look at the syslog in Console, Tinkertool, or Onyx. It did not occur to me to take this approach before.
Thank you BDAqua
The last entry in the console app was launchd com.apple.aslmanager. After that entry, no more entries occurred. The window manager froze, then unfroze for 5 seconds. After clicking, the desktop froze again. The desktop continued to perform in this manner, until I rebooted the computer.
This is the interesting performance issue. What I did, during my testing, was simply read the messages in the console app. I did not open any other application. As a result, the desktop never froze. I opened, the Activity app, to view launchd asl. The desktop did not freeze. I closed the Console app. I also closed the Activity app. The desktop never froze.
It seems that whenever I open more than one application, the desktop freezes after ten minutes. The desktop freezes for a couple of seconds, then freezes again. This process continues until I reboot the machine. For example, I open System preferences. Click on a setting, then close system preferences. I open AppleMail. Download mail, and close AppleMail. I open iTunes. Click on music, then close iTunes. After ten minutes, when I click on another app, the desktop freezes. The desktop unfreezes after one minute or more, then freezes again. On the contrary, if I open an application, and use only the singular application, the desktop does not freeze. If I try to open another app, the desktop freezes.
Hmmm, I wonder if it's RAM?
The Memory test can really only be trusted if it finds a problem, not if it doesn't find a problem.
Memtest OS X...
Rember is a freeware GUI for the memtest ...
I removed DIMM J3 for testing. Ram is now 1.5. The computer operated fine for about fifteen minutes.
The problem began to happen again.
It appears that the desktop freezes for about thirty seconds only when clicking the menu bar in the Finder. That appears to be where the freezes are occurring. The freezes do not appear to occur when clicking the menu bar of applications.
I will download memtest to test currently installed ram.
Safe Boot from the HD, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions.
PS. Safe boot may stay on the gray radian for a long time, let it go, it's trying to repair the Hard Drive
You've probably got a couple of corrupt preference files.
Move these files to the Desktop for now...
where 'xxx' is a 12 digit (hexadecimal) numeric string.
This will reset your Menu Bar to the default, you'll need to go through System Preferences to reset the ones you need. (If they are already checked, uncheck them first and then recheck them).
Finally, this s the type f error I have been looking for. I found this error in the system.log
NVCHannel (GL): Graphics channel exception! status = 0xffff info32 = 0xd = GR : SW Notify Error.
This is the type of error I have been looking for. It is a Kernel  : error.
I will need to log off, to reset the computer, then copy the concluding lines of the kernel failure.
Looks like the device driver(s) do not like GeForce 6200 AGP 256 mg cards. I suppose the preference is ATI cards.
It appears a great many users have encountered problems with the GeForce and NV extensions.
I may need to reinstall 10.5.0 extensions, and update Leopard maintaining 10.5.0 GeForce and NVidia extensions.
I have removed all GeForce and NVidia extensions. Quartz Extreme, Core Image, Rotation, and Quartz GL are no longer enabled. I load extensions, a few at a time, to identify which extensions provide QE, CI, R, and QGL.
I will record my result.