Here's a tweak I made that I think keeps to the spirit.

import random, time, winsound
timebias = 0.2
pitchbias = 0.7
changebias = 0.75

current = [(4.,1.),(5.,1.),(7.,3.),(None,1.), (4.,1.),(5.,1.),(7.,3.),(None,1.),(4.,1.),(7.,1.),(12.,2.),(11.,2.),(9.,2.),(9.,2.),(7.,1.),(None,1.),(2.,1.),(4.,1.),(5.,3.),(None,1.),(2.,1.),(4.,1.),(5.,3.),(None,1.),(2.,1.),(5.,1.),(11.,1.),(9.,1.),(7.,2.),(11.,2.),(12.,4.)]

timeshift = 1;
while 1:
timeshift = timeshift + timeshift * random.uniform(1 - timebias, 1 + timebias)
if timeshift > 1.0 + 2.0 * timebias or timeshift < 1.0 - 2.0 * timebias:
timeshift = random.uniform(1.0 - timebias / 2.0, 1.0 + timebias / 2.0)
key = random.randrange(0, len(current) - 1)
if random.random() > changebias:
if current[key][0] is not None:
current[key] = (current[key][0] + current[key][0] * random.uniform(-1.0 * pitchbias, pitchbias), current[key][1])
else:
current[key] = (current[key][0], current[key][1] + current[key][1] * random.uniform( -1.0 * timebias, timebias))
time.sleep(random.random())
for (p,d) in current:
if p is None: time.sleep(0.2*d * timeshift)
else: winsound.Beep(int(440*2**(p/12.)), int(200*d*timeshift))

Basically, each loop it tweaks the song slightly from the one before it, randomly. The three different bias settings on the top dictate how the song evolves. But besides just changing the song, the rate of any play varies randomly (according to the timebias as well).

The timebias applies to changes of timing. So the tempo of the play, the rate of change of the length of a note and the length of pauses are all shifted by the timebias randomly. increasing this number will create more dramatic swings in time changes from run to run (as well as the overall bounds of the tempo).

The pitchbias applies to pitch changes. Increasing it will let the algorithm drift from the normal song much faster. Too high will cause obvious swings in notes. Too low, and it'll take forever to get a decently maddening change (but perhaps that's part of the master plan).

The changebias indicates the chance that on a particular loop, the pitch of a random note will change, or if the duration will change. This change is carried on to all future plays (and will have a ripple effect)

The result is quite maddening, as parts of the song will randomly trend back towards the correct notes. And notes you could have sworn were wrong will appear normal later. And back and forth it goes. Just repeating, and changing until you get driven mad (or bored) enough to ^C...

Basically, it's a genetic algorithm without a binding fitness function. Its random changes will just propegate infinitely towards chaos. But for a very long time it will have the "feel" of the original song...

I couldn't help myself. I had to have a go at making it, too.
http://jsfiddle.net/GVTk2/

Didn't check it on anything other than chromium, and I can't guarantee it won't eventually use all your memory and crash.
It's horrible in many ways: switches key, misses the frequency of notes, changes from 2^(1/12) ratio between semitones, pauses at random and changes note length.

Take a listen, there's always a chance it'll stop :D

/edit ambiguity. Come to think of it, skipping notes is the one thing I didn't do. Note that it starts reasonably close to being in tune and slowly degrades.

I can't get this to work in Wine. Could you please put up a recording? Thank you :-)

Just to add: (1) The pointless "1*" is because I experimented with other sizes of error too. (2) A slight modification of this lets you, e.g., have the pitch drift downward by 1/10 of a semitone per note, which for me at least is very noticeable and unpleasant even though each individual interval is OK.