DXDiag is this great diagnostic for your gaming hardware. It was created during my time as DX SDK PM by the DX SDK and Tools team. It is hard to imagine gaming before DXDiag and its reporting what is on your machine; but lately I have seen a lot of misunderstanding what DXDiag is and what it does.
DXDiag is a tabbed application that presents information about your gaming hardware.
The front page is the "System" tab and provides general information about what is installed on your machine.
There are tabs specific to DirectXFiles, Display, Sound, Music, Input, Network. and More Help. Each of these specific tabs provides detailed information on that component and all but the Input tab have "Test" buttons to allow you to test the gaming functionality. The results of those tests will inform you as to what the max DX version you can successfully run is. Go to the Graphics tab, and based on the versions it lets you test and what versions pass the test, that defines what Windows thinks your hardware *can run*. Not installed, but what is actually supported by your hardware.