Well, if you have a good running stream with the proper head flow, a micro-hydro generator can be made from scrap parts. Same can be said for wind. Wind turbines on a small scale can be built from scratch and there are different version for different wind options.
Also, with a fresnel lens and some ingenuity (still working on it) a Stirling Engine could be setup to produce energy to possibly run a PC.
Interesting @deanlogic although most of the miners I ran back then had 750Watt power supplies upto 1200Watts +. I can't remember the Amps but I am sure I was maxing out my circuits at 20 to 30 amps.
If anything offgrid can do that , wow!!
Well, I guess the key would be to cobble together multiple options to charge the battery bank that will run the computer.
Granted, the battery bank might be expensive.