Obviously it's your software, I use an ATI card and their software and full screen isn't a problem. I believe Win DVD will use the line-in and that has full screen option.
The VGA box converts an NTSC/PAL signal to RGB so the quality isn true 480P it's actually "stretched" image. To obtain true Progessive scan (2 pass) which the Xbox can handle using the component cables (Red, Green, Yellow) you need either a video card that supports component imputs or an HDTV.
If you truly want the best quality I reccomend using an HDTV over a PC monitor since progressive scanning is superior to RGB + you get higher res and HDTV's are bigger. I use a standard 27' nothing fancy but it is far better than a VGA/SVGA monitor (CRT or LCD).