Technically no. Depending on how loosely we're defining "burning," your mitochondria burn energy-rich chemicals to make you go.

It's a question of quantity and sustainability, not mechanism.

What do you propose instead?

There are only a few fundamental sources of energy (which is a non-negotiable component of "making things go"):

- Nuclear decay (geothermal, RTG)

- Nuclear fusion/fission (nuclear power, solar power)

- Redox reactions (fossil fuel, food digestion)

- Planetary momentum (geothermal, tidal)

I wouldn't call solar power "nuclear-based", unless you want to call most other energy sources (including fossil fuels, wind, tides, ...) "nuclear-based" too (since the primary energy source is the sun, which generates energy via nuclear reactions, of course, but is besides the point)