A commodity electricity can be run without burning. The evidence is current trend of smart/eco houses. Didn't Edison himself powered his estate with waterwheel on a minor creek?
However, the the civil utilities aren't the biggest power consumer. Even now in industrial countries the consumption of energy by population is less than the power requirements of industry.
The factories are highly unlikely to be sated by a few windmills. If you forbid the coal powered powerplants, the industry sites will fall back to either individual generation departments, which might not be as efficient as specialized facilities, or, if that is prohibited as well, directly to coal powered furnaces and steam powered conveyors, which are not only even less efficient, but also reduce the available production methods.
It could be possible to power a factory or two with electric dams but not on the same scale, at least without causing landscape and climate alteration noticeably in process. Other sources, wind, tidal, atomic rely heavily on the availability of advanced technologies and materials. So it is unlikely that Curie followers could construct a working nuclear reactor ahead of induction furnaces, much less likely is someone building a wind generator of industry-worthy scale.
Thus, without fossil electricity, the industry would limp at a fraction of its historical pace. Sciences to a certain extent are dependent on the instruments that are available and would not be as thriving as well.
So, the Earth by today would still be a rural country, with no iphones or facebook, with modest successes in most sciences save for mathematics. Basically what your average steampunk world is.