Emulating systems such as the Gamecube/Wii and PS2 just isn't going to happen with that PC, at least not at a playable speed if you can get anything to run at all, I'm not sure but I don't think the Pentium III supported the SSE2 instruction set which is required for Dolphin.
If you could get anything working you are looking at maybe 3 - 5 FPS if you are lucky, also the FX series aren't supported since they lacked proper shader model 2.0 support, so you'll have rendering issue should you be able to get anything running.
Dolphin requires a fairly powerful PC, an Intel Core2Duo/Quad, i7, AMD Phenom processor is required for the best performance and results, keep in mind that even those with beastly powerful machines experience slowdown in some games.