Okay, this time for the video card I installed something that removed all traces of the drivers. I then reinstalled my NVIDIA drivers with the "Express" option. I changed nothing and, unfortunately, this didn't change anything.
I uninstalled the Roxio software from the D drive and installed it again to the C drive, but this didn't change anything either. (Still happy to rule it out as a potential issue though.)
I installed Roxio on to my 6-year-old Windows 7 laptop, the very same one I recorded from years ago, and the preview came up perfectly. If it comes down to it, I suppose I could buy an external hard drive and record from this laptop, but the poor thing gets very hot and slow. I'd rather use the more powerful desktop.
In the end, it's the same status: audio for a couple seconds then silence and a black screen.
I should also add that I even tried using a different USB port and playing with the PS2 display settings. I have no idea if this would be related to my problems but there was still no improvement.
I just tested an HDMI on the output side and the result didn't change.