What graphics card are you using?
We could start off by downloading and running a basic information utility like cpuz which is available here. The CPU, Mainboard, Memory and Graphics tabs will identify the core components of your system which would give us a starting point.
Looks like it's a Radeon 9550 or 9600. These will support up to DirectX 9. Try running DirectX Diagnostic Tool. Click Start, then type dxdiag.exe in the box. Click on the file to run it. After the tests are complete, click on the Display tab. See what DirectX features are enabled/disabled, in the note box, see what problems are listed. Better yet, include a screen cap please.
I thought hardware acceleration is for browsers only?