Well, after a few hours of struggle I got my 360 working well with my Media Center laptop! Steps taken:
1. Upgrade video driver to v77.79. This was much harder than I anticipated because nVidia refuses to support laptop cards such as the Go5700 (which I have) and said that it is up to the manufacturers. Toshiba, of course, dropped the ball on this one and hasn't supplied any update past June 2004. So, I found this great site Laptopvideo2go which provides modified .inf files so we laptop users can use the latest nVidia drivers. Shame to both NVidia and Toshiba (moreso to Toshiba) for leaving their users in the lurch, and kudos to the people at laptopvideo2go!
2. I finally found a useful article on Microsoft's site describing how to fix the issue I had (corrupt or missing component in my media center installation) at this link.
3. Per that article, I re-installed the .net framework 1.1 sp1 update.
4. Then I re-installed Media Center 2005 Rollup 2
5. Then I re-installed the XBox media center extender and re-setup the connection between the 360 and my laptop.
And....it all works! So now I just have to hook my laptop up to my cable box and I'm good to go on using my XBox and it's connections to the TV and stereo to watch TV, record programs, listen to all the MP3s on my laptop, etc etc..
First impressions are that it is all working quite well, although the timelag between remote control commands and actually performing them is noticeable. (That makes sense though, since it has to go from the xbox over the network to the PC then via the IR controller to the cable box.)
So, everything's configured and running smoothly. See you around on XBox Live! Feel free to send a 'hello' message to Twilight Sky if you get a chance.