The FX series don't have proper shader model 2.0 support, it even fails to render most PC games correctly that require and utilize shader model 2.0, this is why the DX9 plugin won't work.
It also lacks the required version of OpenGL and it's associated extensions, so you won't be able to use the OpenGL plugin.
The only choice is to upgrade, a decent PCI-e graphics card which can handle Dolphin, can be bought for $50 - $100 give or take a few providing your system has a PCI-e slot.
Also your processor is a bit on the weak side, if you bought a new card games will likely run slow and some games might run half speed at most if you are lucky.
I thought I should explain this a bit further as to why it won't work.
It also lacks the required version of OpenGL and it's associated extensions, so you won't be able to use the OpenGL plugin.
The only choice is to upgrade, a decent PCI-e graphics card which can handle Dolphin, can be bought for $50 - $100 give or take a few providing your system has a PCI-e slot.
Also your processor is a bit on the weak side, if you bought a new card games will likely run slow and some games might run half speed at most if you are lucky.
I thought I should explain this a bit further as to why it won't work.