rooted

Chell is definitely still alive.  When we see her view of the outside (even though she is laying motionless) we hear that bird-twittering sound they use in the old Looney Tunes cartoons when a character gets knocked over the head but is still alive.  I don't think the sound was meant for GLaDOS, and it was too light-hearted and comic to accompany the death of the player's character.  Also we know GLaDOS was still alive way down deep in the underground complex because the previous clip showed the camera zooming down and all her eyes blinking on.  GLaDOS's song says that Chell left her but GLaDOS is happy inside, and that GLaDOS doesn't envy Chell in the outside world.  GLaDOS seems to struggle with reality and sincerity and I doubt she even knows what they really are.  If GLaDOS's song seems overly pleased with her success then I think it is just her constant self-deluding optimism!