Power source: Ehh...
Let's chop out the bit about how gargoyles are bound to a building. This thing isn't bound to a building, it is a building. This thing is as big as a cathedral, and when it turns to... ice in the light of day it is safe to enter.
And no power source either. None of them are really clicking with this "big building-monster thing" idea that we've got going on.
So it has a symbiotic relationship with a small group of people, I imagine. During the day, they take shelter in its icy organs and protect it from vandals and raiders. When the sun falls and it reanimates, the cathedral beast protects the people. Perhaps the people also feed it by leaving some of their food in its stomach before they depart for the night.