At the very least, we know the brain obeys the laws of physics. A computer can simulate the laws of physics. Therefore, a computer can simulate the brain.
A computer can estimate the progression of physical systems, but cannot solve for all but a trifling few. (think three body problem). In some cases, we can estimate to an arbitrary degree of closeness, but in many cases we cannot (or at least cannot know that we are). This is the norm for complicated differential equations. An estimate which seems to be arbitrarily close to a solution might in fact be very far away. And these inaccuracies can compound and cascade in a massively parallel system like the brain.
Until we know more about just what aspects of the brain are relevant for the mind, we will have no idea of how limited the prospects are for a computer simulation. The problem may not be one of computing resources, but of fundamental limitations in the mathematics of computation.