neuroscience - Which part of the brain needs to be shut down to lose conciousness?

There is no widely-accepted neurological structure that mediates 'consciousness.' Even if some structures have been shown to be necessary for consciousness, they have not been shown to be sufficient. This is true with anesthetic mechanisms as well -- their ability to paralyze and block pain signals is fairly well-understood, but the mechanism of loss-of-consciousness is still unknown.

Still, 'consciousness' has to be there, somewhere between being awake and being dead, states which anesthetics can readily bridge (review):

Nevertheless, at some level of anesthesia between behavioral unresponsiveness and the induction of a flat EEG [indicating the cessation of the brain’s electrical activity, one of the criteria for brain death (22)], consciousness must vanish.

Later in the same review:

The evidence from anesthesia and sleep states (Fig. 2–3) converges to suggest that loss of consciousness is associated with a breakdown of cortical connectivity and thus of integration, or with a collapse of the repertoire of cortical activity patterns and thus of information (Fig. 2). Why should this be the case? A recent theory suggests a principled reason: information and integration may be the very essence of consciousness (52).

This is consistent with my own take. Consciousness itself is the subjective experience of 'brain,' so it can't be lost, just poorly integrated.