Bill,
If the computer has only a single VGA port on it, I do not believe the splitter will give you the functionality of using both monitors separately. It will do one of two things based on the quality of the splitter:
1) give you one useable screen and the second will be an exact duplicate of the first, but with no functionality
2) let you use either as the main screen with full functionality, but not both simultaneously.
You are basically splitting the single output of the on-board graphics, and sending the exact same display to two different monitors by splitting said output. The computer will not recognize this as 2 different displays and can not give you the functionality of using them simultaneously. As far as I know, the fastest and cheapest way to accomplish what you want is to add a graphics card that supports dual monitors.
If you'd like to post the model # of the desktop system, we can help you identify on that will work.
"Friends don't let friends dial-up"