They screwed up the continuity there a bit. Palm rode the elevator up using Bizeff's code but later they say if someone enters a code that doesn't match the height and weight of who it belonged to then it locks down.
The scene you're talking about starts at 20:13
That song is one of my favorites, its name is : Reason ~ Instrumental
(Yeah it is the instrumental version of the ending 3)
Here is a link : https://www.youtube.com/watch?v=I7uXsgsZlps
(The part you're looking for starts at 1:05)
It is also played when Kirua fights Rammot