What is it like to be a Bat?
If we now leave all the controversy beside, then we can at least say, that it seems that there are thought processes which we don't understand and which we can't access directly via the neuronal system. It may well be the result of physiological processes which we, as claimed by Nagel, don't understand yet.
Let us for now assume that there are different levels of how the mind can be access; some levels can be access via sensory or cognitive processes etc. (easy problem) but others not (hard problem). If we now assume that consciousness has a physiological origin then that means that distinguishable physiological systems must exist which correspond to the hard problem or the easy problems.
The existence of different systems or "levels of consciousness" may as well be reflected in the memory system. Memory is an integral part of computation and its clock rate may correlate to that of the computation. Because the brain organizes memory in different system ranging from short to long term memory, those memory systems may work in different space and time scales. Then, they must operate quite differently.
For now, we conclude that, if consciousness is a physiological computation, it consists of different systems. One or more of the physiological systems should correspond to the "easy problems" part. This part is directly connected to sensory input and processing; a system which operates within the neuronal network.