Top: Early workstation-type system with rolltape monitor using large rollers, and teletype printout display modes.
Middle-left: “Portable” mecha-computer table with miniaturized rolltapes in its display system. Power supply via compressed gas or other power-carrying fluid; this seems like the most flexible power supply option.
Bottom-right: Plug-in power supply via a rotating drill-like shaft that plugs into a socket. Heavier and requires keeping the computer stationary, and more dangerous thanks to the rapidly spinning shaft, but maybe better for heavy duty power transfer?
Computer operation is, I assume, via gears/shafts system a la the K’NEX computer and various LEGO pure-mechanical circuits, potentially highly miniaturized using similar techniques for machining watch clockwork. Initial idea was taken from the Zuse Z1 computer, though I remain unclear on how it works exactly. Potential complications with mechanical systems: efficiency of energy transfer. How often are mechanical signal amplifiers needed to maintain a digital signal? How might this limit complexity and/or miniaturization of a mechanical circuit of given physical size?
Other systems using fluids and other media are possible but I am not sure how well these would scale to large computer systems. Gears and shafts seems most intuitively obvious to me.