Your graphics chipset is too old to even use the DirectX plugin, I should know as one of my old computers had that chipset. It can't even play games such as unreal tournament, quake, or the old Rainbow Six gameswithout major lag, the thing can just barely render the desktop.
It also lacks any kind of shaders, Dolphin requires a graphics solution that supports a minimum of shader model 2.0 just to use the DX9 plugin. You can forget about OpenGL all together since Intel chipsets aren't supported by the OpenGL plugin.
Also your CPU is so crap that even if you could boot any games, they would run no faster than an utter slide show, I couldn't imagine you being able to squeeze anymore than 1 FPS at most in Dolphin out of that ancient low end processor, even with a decent graphics solution.
You can't honestly say you thought you would be able to play Gamecube/Wii games on that system when it can't even play any PC games made in the last 5 - 7 years and even has trouble with most/all older PC games. If it can't even play those game what would make you think your system would even be able to emulate the Gamecube/Wii when they are last-gen/current-gen hardware?
Emulation is far more intensive on resources than playing PC games natively, so if your system isn't able to handle PC games made in the last millennium then it also isn't going to be able to handle emulating last-gen/current-gen hardware.
So you either have to build or buy a new system, however buying a Wii if you don't already have one would be much cheaper than the hardware you would need to run games somewhat decently in Dolphin.
A new Wii is $150 - $200 used while the hardware you would need could run up as much as $700 - $1000 or more.
If you still insist on playing Dolphin, try to stay away from anything that is pre-built unless you review what hardware the pre-built includes before you blow your money on something that may not perform well.
Go Nvidia or ATI and stay away from Intel's crap graphics solution, for a processor a Core2duo is recommended for best performance, to save som money you can buy one of the cheaper models and overclock it.