I don't know the version on the video, but the original is "Sadeness", by Enigma, a big dance hit in the late 80s-early 90s. Funny, I only heard the original for the first time in ages last weekend and it brought back some great memories!
Edit: The two guys above beat me to it, and maybe it is the original, though the intro doesn't sound like it. . . I did a search on Limewire and only came up with the Enigma version.
[Edited 2006-01-19 00:19:08]