SDI features the music of L'Arc~en~Ciel, the Japanese Rock band who did, among many other things, the second song heard during the Spirits Within's credits (this same song).  I presume the video was made and released to Music Video broadcasts (or at least MTV) around the same time as the movie.

The video is basically the Deep Eyes performing in place of the actual band, in various familiar places, interspliced with film clips out of the movie.  The setup looks to be - Gray, vocals; Ryan, bass; Jane, guitar; and Neil, drums.  All of which have taken the part (and instruments) of the actual band - Hyde, Tetsu, Ken, and Yukihiro, respectively.

It comes in both the English and Japanese language versions of the Spirit Dreams Inside, but both are the same, visually.  It is highly amusing, and proves several things - such as you can fight off Phantoms with guitars, or that the crew really did live through the end of the movie...  (Shh!  They did!  Really!)

How can you see this video?  I don't think it's on MTV anymore, but I presume it's still circulating the internet on filesharing programs such as Kazaa and eDonkey.  Alternatively, you can download a small version on site.