I'd start by checking to see if my neigbors experienced anything simular.
as to what it could be, I've no idea. waht kinds of things came on? lights, motors, all of the above?
lights could be explained by emissions, I think. (have you ever put a florescent bulb in a microwave? it lights right up.)
sounds a lot like the 'haunting in georgia' show from friday night discovery chanel