You stated that:
One last thing. When I use my laptop to network I am able to get into the desktop and access files when it is in the shutdown mode with light on.
That says to me that the operating system might be OK - but that either the video card is bad, or that the monitor is bad.
I think the PC is really still running when the screen goes black, you're just not able to see it.
Let's start with the easy one... can you borrow a computer monitor from a friend and see if the problem goes away?
If the screen is not the issue, you may have to try a replacement video card... which is a little more complicated to change.
Meanwhile, can you tell us which ZT computer model you use?