Downhole power delivery tool powered by hydrostatic pressure

Certain aspects are directed to downhole power delivery tools using hydrostatic pressure within the wellbore. In one aspect, a downhole power delivery tool is provided that can be disposed in a wellbore through a fluid- producing formation. The downhole power delivery tool includes a body defining an inlet proximate to a chamber in the body, an actuation mechanism in the body and adjacent to the inlet, and a piston proximate to the chamber. The actuation mechanism can allow communication of hydrostatic pressure via the inlet to the chamber from an annulus external to the body in response to an actuation force being applied to the actuation mechanism. The hydrostatic pressure communicated to the chamber applies a first force to the piston. The piston applies a second force to a rod movable relative to the body in response to the first force being applied to the piston.