Are you copying from an original disk? If so, nero recode would be the best program to use to burn as it is designed for copying dvd's, plus like shrink, it can compress if nesasary.
Once you have copied the file to your computer, put them in a folder called VIDEO_TS. in nero start smart, find the icon "copy entire dvd-video". That should copy the movie properlly. By the way, if you have anydvd running, it is usally not nesasary to to copy to the hard drive manually like that. Just use the "copy entire dvd-video" option, find the VIDEO_TS folder on the actual dvd that you want to copy and select it to import. anydvd should run in the background and take care of the copy guard. This should work for all except for a few of the latest macrovision protected movies.