Or there is more to reality than we know... yet. There is probably yet another force to exploit for computation and communication, which can also be treated with materialistic techniques.
http://www.aei-potsdam.mpg.de/~mpoessel/Physik/FTL/tunnelingftl.html
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html
I don't think there is a single scientist in the world who thinks mankind knows everything already. What point would there be to waste time looking? As far as I can tell, only young-earthers and such believe they know "everything".
Therefore, there could be additional forces that (when properly modelled), turn out to be even more useful than electricity. Of course, they'll have to be about as repeatable as electricity to be useful to anyone.
So far, I can't think of any non-materialist models that produces anything repeatable.
Can we ask a psychic what will happen tomorrow? Yes, but you may as well have rolled dice.
Can we apply telekenesis to move rocks, or would bulldozers be slightly more effective?
Shall I build a bridge according to Feng Shui, or more conventional engineering and material studies?
I've got a great idea: a digital electronic computer is only one way to build a data processing device. They can be (and have been) built based on a wide variety of switching, fluidic, mechanical, nervoud, etc. models. There are many possible methods (not all practical) to send signals over a distance, as well.
The challenge: Build and demonstrate a data processing or communication device without using any 'materialistic' assumptions.
I fear those pesky computers, radios, TV sets and telephones have set a very high bar of expectation for your creation. Something that can barely beat random guessing in a short, poorly blinded and inconclusive run of tests won't convince anyone that you've invented a new telephone. At least, not anyone without squirrels in their brains.