You need to go to the side of the building and find a way to get to the most bottom floor. There you will see a garden with a glowing flower.
Pick it up and carry it into the tower's first (lowest floor), you will see a generator there that works like a crafting station. Put the glowing flower there to power the tower.
Then the buttons (elevator) will work.
Pay attention to the song lyrics found all over the tower floors. At the very top you will need them.
Which brings me to the next question. What was the point of this place?
There was no story loot or even good regular loot.
