We need a little more information.
What is the Model number of the Compaq Desktop?
What CPU are you using?
What kind of motherboard is installed?
How much memory do you have installed and what kind (DDR, DDR2, DDR3)
What is the Power rating of the PSU and what is the amperage rating of the 12V rail(s).
How much money are you willing to spend on a new graphics card?
All of this information will help you get better recommendations.