I tried to import DVD audio to Cool Edit but every time came audio in english mixed with background music. There were 4 different languages on DVD I tested.
Cool Edit recognised audio files that already were mixed (speech + background music)
Why only English version? Why wouldn't it import others? I don't know! Strange.

I'll take another look.
Back to alternative solution:
You don't need actually to play audio in Cool edit for recording in Cool edit.
Play your DVD in Power DVD or what ever and keep Cool Edit open as well.
In that way you can record everything you hear on your PC.
Choose your language and play dvd. Cool Edit will record it. (adjust your sound card for “what you hear” recording. (In window mixers recording control choose where you are recording from)
In your case it will be neither MIC or LINE IN.
If you don’t have option what you hear then try different options. Try CD or … try them all.
Still, I think you’ll get this background music in your record.