The thing you are both referring to, and yes it is the same thing, is what is called the "Major General Recap." It is a parody of the song "{I am the very model of a} Modern Major General" from the above-mentioned operetta by Gilbert and Sullivan. They did a pretty good parody, right down to the insanely fast speed and constant throat-clearing. I recommend seeing the play or getting the soundtrack. I did both, only because I heard of them from ReBoot, and was pleasantly surprised.
You can download a copy of the original song, and try to find the ReBoot clip you're looking for, from any of the file-downloading systems such as Kazaa, if you so desire. They have a partial version somewhere on the Mainframe website, but it ends after Bob and Matrix meet up and take a bow, because they "really were delighted guys." I have a copy of the full clip, as well as the sound byte of Mike's introduction, somewhere among my disks. If you want me to try and send them to you, feel free to contact me on ICQ by my nickname (and don't die of shock now...) Permanently Confused.