機械計算機

There is such a thing as a 機械計算機. Ideally, this type of computer would undergo the shrinking process which electrical computers have. Astronauts relying on 機械計算機s may need to carry lookup tables with many needed calculations already figured out. 機械計算機s were actually the computational device of choice for a long time, until vacuum tubes became more readily available.

機械控制

Such a rocket ship would need 機械控制. Gears and springs would still work in low-gravity, but are quite heavy. Extreme metallurgy, ceramics, or plastics would be needed to make such a craft functional. It is, at least, theoretically possible have a rocket use purely mechanical processes to guide itself.

化學

Nota Bene: Electricity simply "not working" does many, many terrible things. For instance, the action potential our nerves use falls under "electricity working." This means all animals would have the reaction time of plants, which are known for not reacting to stimuli quickly. I would suggest re-thinking how much "electricity" you wish your world to have. Taking a hard look at what type of story you want to tell or your audience is critical here.