Okay. Well, I'm not at home right now so I'll post it tonight. Thanks for the help. For now, I can use this as an example.
The image above is what my Dreamcast is using. That plugs into the Roxio.
Then a set of cables that look like the image above go from my Roxio to my television. With that setup, I get the Dreamcast running on my TV perfectly fine. Theoretically, that should mean it's working, but when I plug the Roxio into my laptop and open the capture software, it says 'No Signal' and the preview screen is just pure blue. I do however get the audio from the Dreamcast, coming through my speakers.