I have an older system (built in 2000) on which I am required to hold down the on/off button to shut off the power after Windows XP is finished shutting itself down. Is there anything I can do to make it shut down automatically when Windows shuts down like my new system?

Check this Microsoft knowledge base article.

http://support.microsoft.com/?scid=kb;en-us;313290&spid=1173&sid=156

This could very well be the situation with your older computer.

I don't have an "APM" tab in my "Power Options". It seems that the system may not load an ACPI compliant HAL. I updated the BIOS about a week ago so I’m fairly sure I have the latest one. I guess it's time for more research. If I find anything I will post it.
Thanks for the input!

   I would think that is a hardware thing.  If the computer is not made to shut down automatically, I would think that no matter what you do with the BIOS or system, it still is not going to shut down.  The only solution would be to get a newer computer that was designed to shut down automatically when Windows shuts down.

Thanks Ray, I was hoping that there was a work around that I was missing but I had a funny feeling I was stuck with it.

Depends on the computer manufacturer. See this article for details.

http://support.microsoft.com/kb/810903/en-us

dlwolff0 you are the BOMB!!!

This was the one... http://support.microsoft.com/kb/810903/en-us

NTApm/Legacy Support was not installed. Once I manually installed it with the Add/Remove Hardware tool in Control Panel, the system shut down by itself. Thanks!   Cenzo.