A TV card should do this, correct? One of those USB jobbies. I can remember using an Xbox on a Dell with a Hauppauge TV card. But the big drawback, it was laggy because the TV mode was in a small windowed screen so when you enlargened it it looked like crap and performed bad.
Edit, now I think of it this would be a poor choice since the 360 would not be able to utilize HDTV mode even if you were to go through all this.