Insulators can allow for, effectively the same method of electrical transmission we use now... in fact internet and phone cables are laid on the bottom of the ocean to connect the continents of earth.
Fun Side Effect (well to me anyway :D ):
Having stated the above I would add that it would even be possible to pass a controlled current through a tube built from an insulator that is filled with nothing more than sea water. Wires attached to, or as part of, a device would be most effectively water tight. Though, also pretty interesting, I don't think a 'power leak' would actually prevent power transmission. Instead, I'd conjecture, this would cause a great deal of attenuation in the amount of power carried.
Using water as the means of power transmission may be valuable but I suspect it would have limits in a computational device. Forming tubes of smaller and smaller sizes would be one likely limit. The boiling point of water might be another... I don't believe steam has the same conductivity profile. So in the end, for building small, fast and efficient computers, I suspect the race would discover some other, semiconducting, material (silicone does seem like a very likely choice) much as we did.
Short answer, just insulate.
Oh, also, while I had thought it before I saw the comment, I wanted to point out that this was said in a comment by Cort Ammon as well.