Brian,
Electric powering of your dob is possible however all critical components must be properly enclosed and sealed.
Military style connectors, boxes and so on are a way to go.
Mechanical drives were common at the beginning of the last century... However they were heavy and cumbersome, and for equatorial mounts only.
To design a mechanical tracking mechanism for dob (both axis must be driven) would be a great challenge...
So your only solution to this problem is battery powered computerised system, properly sealed.
Or EQ platform, as Rob suggested (again, properly sealed, plastic gears and so on).
It should not be a great challenge to design a stepper motor with simple (plastic) gearbox, driven at appropriate rate (microprocessor controlled) for the eq platform.
Alternatively, Bartels system can be used - but properly sealed, of course.
I think that even a Synscan unit is sealed... I am not sure how well, though.
Long time ago I used a mechanical clock from two-tariff electrical power meter - they were completely mechanical, self rewinding (powered from AC) and the torque was significant.
I am not sure if they can be found these days anywhere..
EDIT:
Now I see on your signature that you have eq mounted 8"..
So, one uController, one stepper driven from that and plastic gearbox driving your eq mount, all that powered from rechargeable battery should do.