It should work. Most AGP boards till in use these days have AGP 4x or AGP 8x, and 8x cards will work in 4x boards.
That being said, you should know that the x1650pro cannot handle recent games. It achieves a horrible 3.7 fps in Oblivion for example. Consider an x1950Pro or x1950xt, even if they cost more and require a more powerful PSU.
What CPU do you have, and how much RAM? If these are not good enough then the x1950 cards would be bottlenecked, and you're better off just building a new system from scratch.
You can get some details from "My Computer". Find it on your desktop, right click, select Manage. Or click the Start button, select Run, type msinfo32. It depends on your version of Windows.