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Can I use the movies that are stored on the file computer via a Mini Mac?

Yes. You can mount the XP movie share on the Mac and then use the DVD player app on the Mac to play a set of VOB files in a dir.

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Would I have to modify the XP box to do it?

No. Just plain Windows file sharing will do since it doesn't need to know what the files actually are.

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Would I use Samba?

The Mac might use Samba behind the scenes but you don't need to fiddle with it.

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Is it easy?

Yes. I do this with a Samba NAS and my Mac mini. It is a bit clunky since you have to mount the share and then select the directory in DVD player. You might be able to find some nice front end that does this for you however.