The Radeon HD3000 series are too old to support modern GPU video decoding via DxVA.
The 3000 series parts are either "UVD" or "UVD+". You need UVD2 or later to use GPU decoding feature of Chrome/Firefox/VLC/etc. You may still have 3d accelerated graphics, but your GPU does not have the hardware parts to run modern GPU decoding.
Also, AMD has stopped releasing feature update drivers for the HD3000 series GPUs. They were deprecated a long time ago. HD4000 series is also deprecated. The oldest GPU you can use nowadays and receive up-to-date drivers (including new features, improved performance, etc.) is the Radeon HD5000 series, "Evergreen". That's two generations newer than the one you have.
Finally, there is a diagnostic tool (freeware/donationware) written specifically to evaluate your DxVA (DirectX Video Acceleration) situation, meaning, which API level is supported (if any) by your driver/hardware combination, and it will even tell you if you support the feature level required by Adobe Flash.
It's called DXVA Checker.