Can't they put a cat5 down there, and like a mini router? Or run an antenna down?

802.3 distance limitation: 100 meters. Only about 2200 meters short!

This is actually a bit of a fascinating question. Even if you found an appropriate technology, I would think mist cable would break under it's weight (I don't know if it would hanging straight down). Even if you got a cable sown, what would they hook it to? And I'm not sure I'd want to have a cable stuck in the only hole I have that's gotta serve for anything else that I would want to get down there.

It says there are three holes, so I'm guessing at least one is dedicated to hoses.

Easy. Dialup. A twisted single-pair phone cable can be/is extremely light, and I'm pretty sure they can transmit that far.

Of course, the engineer in me wants to know how well sound waves propagate down the holes, and wants to implement dialup or DSL with actual sound waves

They have optical cable.

You apparently haven't heard of my neutrino-powered wifi transmitter.