It's already possible to tweak the process parameters to produce slow-but-efficient chips. I recently saw http://www.ti.com/lsds/ti/microcontrollers_16-bit_32-bit/msp... : 45 microamps/MHz up to 4MHz, runs down to 0.9V. Pair with a suitably low self-discharge battery and it'll run for a decade.
There's also general-purpose designs like Intel's Polaris[1] 80-core CPU that's close to a decade old (GPUs of the time had 320 cores, so a modern Polaris might scale to 1024 cores).
Making neuron-like massively parallel hardware is one thing, making software to run on it another – we seem to have misplaced the source code to the human consciousness somewhere, alas, and reverse engineering is taking its time.
Perhaps what would help is to store energy locally, like our brain. Each cell has its own store of ATP, so a constant feed of ionic current is not needed.