To add to Shevliaskovic's answer, after listening to the song, I notice that after the G major chord that you cited is followed by C minor. So that can explain the eventual move to G: To resolve to C minor (a V/i relationship).
I think if you consider the G# chord to really be an Ab, it might put the two chords Cm and Ab into a closer relation. As for the F? Is it IV of i in C minor, or VI/I in Ab? Either way, it's an altered (and beautiful) chord. F minor, which fits diatonically with these two keys, finally appears around 2:53.
Melodically, during the C minor vamp, the note Ab is very prevalent. It's so far a tug-of-war (so to speak) between C minor and Ab major.
Next, Eb major is emphasized (III/C or V/Ab), resolving to the beginning section in Ab, but then coming back almost as a tonic at the end!
So we have three harmonically closely-related sections of this song that are C minor, Ab, and Eb. Perhaps this could be best thought of as a fantasia. It ends on Eb but I'm not convinced that is the key.