The problem happens when I go to shut down. After seeing the "Windows is shutting down" screen, the monitor shuts down but the tower stays ON. I just replaced the power supply and the trouble continued. It acts as if something is attempting to restart. Please advise.

Have you checked the power settings in your BIOS?

Thanks for the suggestion. Yes, I did check the BIOS, but I am not certain just what it is that I should be looking for. Would it be under the "Advanced BIOS settings" or "Power Management"? Or some other setting?

I would guess "Power Management"

Do you know the ID of your motherboard?

Or have the manual on hand?

I would like to thank all of you for your input. Since I could not find any problem with all of your suggestions, I took my tower to a shop that is VERY good and HONEST. They checked it out at their shop and could NOT duplicate the problem. When I left it with the tech, he mentioned that it could be something as simple as the power cord. When I got home, I was cleaning up under the desk and noticed that the cord was barely stuck into the socket. I must have kicked it as some time recently. I picked up my tower, plugged everything in and it works just like it supposed too! Who would've guessed. Thanks again.