I own this album. Popped it in for comparison just to make sure I was thinking of the right track.
Bump 1744 - "Opening Typo" http://www.bumpworthy.com/bumps/1744
Artist: Jackson and His Computer Band
Album: Smash
Title: Radio Caca
It's the last track (16) on the album. 20:16 in length, but the song only runs until 4:43 and then is followed by silence until the "hidden" track starts at 18:47 and runs until the end of the track. The section in the bump clip is 0:42 to 0:57, but repeats almost verbatum at 3:26 to 3:41, so your guess is as good as mine as to which one they used. By the way, this artist is absolutely brilliant. A good chunk of his song use a technique of sampling single notes or orchestra hits or vocal clips of less than a second each and composing a "chopped and screwed"-esqe entirely new composition out of them.
Thank you very much!! I knew I recognized the music but I wasn't sure were it came from. The info has been updated. Welcome to the forums! :-D