All you need now is a small solar panel and battery set-up and you can be mining bitcoins for no operational costs.
I wonder how long this could run off of just a 12v car battery. Or a bank of LiPos.
For fun:
Let's take a group 27 deep-cycle battery from my store ($117.95 + $5.00 core charge).
It's rated at 96 amp-hours, multiply that by its nominal voltage of 12 volts and you get 1152 watt-hours.
Divide by 36 watts (we'll assume that the DC-DC supply you'd use in place of the AC-DC supply will also pull 36 watts from the battery) and you get 32 hours of run time (approximately).
You'd want to use a deep-cycle battery, not an actual car (cranking) battery. The car battery wouldn't last very many cycles in this application.
And LiPos are just too expensive for something like this, several times what a wet lead-acid would be.