Well, those are all different modes of the same key signature (no sharps/no flats) so your question is more related to harmony rather than key. The harmony does indeed change through the basic chord changes that occur during the piece.
If I'm not mistaken, I'm guessing the piece is based on E natural minor (I'm guessing that because I remember hearing an F# somewhere in the arpeggiated electric sitar, I believe), which makes it the key of one sharp, which is also shared by modes like C Lydian, G Major, B Phrygian, etc.
Then again, I'm just guessing, I haven't heard the song in a while, but I think I'm pretty right. Either way, its in some sort of E minor.