LP'ing Gamcube games

As you may or may not know Mr. Freeze and I have been planning to do an LP for Soulthrow's youtube channel and we finally agreed on a game. The only problem is that it's a Gamecube game and neither of our computers seem to be strong enough to play it smoothly. Does anyone have any bright ideas on what equipment we may need for an alternative method? and blame Freeze for suggesting to put this in the general gaming section if it's wrong

Wouldn't you want to get a screen capture device to play it on the console?

That's the intention at the moment. Know any good ones or where we could possibly get one?

No, if I did I would have one so I could do an LP of SSX.