This ones a little out there, so it might or make too much sense, but I will be extremely surprised if it has been done before.
So, inside of a star, there is rare material x, which when going through a process (idk maybe melting it down or something?) produces a type of extremely powerful energy that is so much more powerful than electricity it completely ...
Something For Nothing?
You can't get energy from places where there isn't energy. Ultimately, energy in almost any form comes from stars. The forms of energy we use are all the stuff we're likely to use. So it depends on how far out you're looking for tech. I'll give options for various alternatives at different tech levels.
Most of the stuff listed by Allan ...
There are a lot of non-nuclear forms of energy with our current technological abilities. And nuclear can be divided into two types, fusion, and fission. It is plausible to have fission without dirty waste say using Boron-11 (it is always 20 years away).
You mentioned solar and wind, there is also:
Tidal and wave action
Biomass chemical ...