You folks have no idea how much I appreciate all the suggestions. I was frustrated last night and didn't do a lot of troubleshooting.
To begin at the beginning, I built the box in either 2004 or 2005 and used what were good components at the time, but everything is a bit dated by now. Additionally, I have always run some sort of DC....Distributed Computing.....program like SETI, or Folding@Home, so the box ran 24/7 for a number of years.
It is a 478 Northwood chip on an ASUS P4P800 mobo with a 37GB HDD and 3GB of ram.
More recently I have added 2 GB of RAM to my existing 1GB of ram but can't think of any issues that came up.......immediately. I add the qualifier because a few weeks after that the box would restart over and over and when I finally got it to stay on I couldn't get it to shut off.
After that I added a utility to monitor temps that showed my graphics card temp in addition to my cpu temp as MBM(MotherBoard Monitor) does. That is when I noticed my graphics card was very hot and stopped running the box 24/7.
As for POSTing.......I don't even get what we called the 'happy beep' when I power up.
One of our folks suggested restarting and hitting the 'TAB' button, saying that might show an error message, which I will try first. This is something new to me so I will probably try it first.
Next I will try removing the new memory and/or replacing the old memory with the new memory and then move onto unplugging other things to see if I can isolate the problem, even though I bought the suggested memory modules.
Thanks again for all the advice, and don't hesitate to offer more.