1: Apple DVI to Video Adapter http://store.apple.com/1-800-MY-APPLE/WebObjects/AppleStore.woa/wa/RSLID?mco=16193109&nplm=M9267G/A this will show the pictures...
For sound. u alos need this airPort Express Stereo Connection Kit with Monster Cables http://store.apple.com/1-800-MY-APPLE/WebObjects/AppleStore.woa/wa/RSLID?mco=4D3ECD40&nplm=M9573LL/A i know it says its for airport, but it works, i had is working, so u have sound and video.
OR
2:Apple AV Cable for iBook http://store.apple.com/1-800-MY-APPLE/WebObjects/AppleStore.woa/wa/RSLID?mco=E4710366&nplm=M8434G/A
i never tryed it with mac mini, so i am not 100% sure....u can have a try...