If our hypothesis, that the brain has an unknown computing network, is right then the question is how can this be possible? Which are the physiological mechanism involved and which mechanisms could be overseen by neuroscientist ?   
Two mysteries 

To find this or those systems related to the hard problem, we have to ask which physiological phenomena are essential for consciousness without being directly connected to neuronal cognitive and sensory processing.  
This is maybe most obvious, but we believe essential to understand the mind. It is the heart beat which is a necessity for consciousness. 
Neurone firing is robust against small disturbances like this. Therefore, one can conclude that there must be a system which depends strongly on blood flow dynamics without directly influenced by neuron processing.

2. Hypothesis: quantum computing

If we look out for an unknown computational networking in the brain then the first question is why have neuroscientist overlooked it since now. The necessity, that the brain must be conscious,  may complicate the experimental observation. Another possibility is that it is not observable classically.  Although research in cognitive neuroscience has recently shown that the mathematical formalism of quantum theory can be adopted to model  cognition showing advances over  traditional classical probability theory  in many aspects of cognition such as     to mention only a few.