Will my PC run anything up to and including Gamecube games?

I'm new to the emulator world and I originally was thinking of building a dedicated emulator PC to just keep in my TV console. However, since I just built a pretty good gaming PC (one that sits right near my TV) I thought why not put it to good use. Here is what I've got.

Intel i5-3570K OC'd to 4.5Ghz (on water, can push higher I'm sure)
Nvidia Geforce GTX 670 FTW edition
8GB DDR3 RAM

I'm guessing this is powerful enough and I'll just need to buy a DVI-HDMI adapter but I wanted to be sure. I also wanted to at least find out what are the minimum specs needed really to run all games up to and including Gamecube games in case I decide I'd want to just build a dedicated emulator box. All suggestions are very much appreciated. Thanks.

This will be powerful enough to run any available emulator for any console.Including the PS2 (On pcsx2 you should tweak the settings to fit your specs).Yeah and it will run the gamecube.