Question: I've been reading through other posts about such megastructures and they're getting me part of the way to my destination. Wanted to see about a few specific options my imagination has latched onto.

The original concept is a tower, an arcology with a 1 km base level (willing to taper it as it gets higher if necessary), reaching to at least 8 km altitude. 

Assume that available power is not an issue.

One idea is: Blocks, rectangular or triangular prisms, containing powerful electromagnets that are the 'mortar'. I liked this option because the society is ancient, and a blocky look fits the aesthetic better, masking the futurism. I realize it is power inefficient. Would such a thing work on this scale?

Thanks!

EDIT to reflect excellent comments: 

Trying to avoid elegant solutions such as Space Fountain, Space Elevator, etc. We want to solve the issue of structural stability with brute force as much as possible. Would a system like this hold up versus gravity, bending and torque at high altitudes?

Answer: 
Easy peasy. Basically, you want lucid dreaming with an I/O interface.

(Note: If I can dodge work enough I will try to find the New Scientist sources for this to add to the answer later, but I have read articles on all these three points recently)

You simply need to rig up a brain interface into the optic nerve. There is recent technology that can show a grainy but identifiable image of what someone is looking at simply by measuring brain waves; that gives you the output part. 

The input part you'll have to handwave, but it's not too much of a stretch to come up with something that can trigger specific images.

As for the immobile part, that's exactly what the body does naturally during REM dream sleep. So simply plug in your I/O helmet, trigger the body's natural REM state to immobilise your muscles, boot up the lucid dream for the world you want, and voila!

This addresses the comments I've seen here a few times - about the difficulty of immobilising muscles, and about fast/fine control; I have incredibly vivid, occasionally lucid and almost always sci-fi dystopian dreams, and I can confirm that I can walk, run, jump, fly, fight, drive vehicles, fly planes etc etc etc and all without falling out of bed, and I'm pretty sure everyone else here can too :)
without moving their own body is the tricky part, that requires severing the signals to the body which is not something down easily or lightly. or course sticking them in a big sensory dep tank and letting them move is an option.

Eventually we will be able to do what you want, but we are talking the level of printing a body from scratch levels of tech. A level of tech where a severed spine is as easy to deal with as getting a tattoo today.

You would have to spend weeks of not months just having your synaptic pattern mapped by an AI just so the inputs can match what your body already does. It is possible this could be done while you go about your everyday life however. This in and of itself could have utility in diagnosing sensory and other abnormalities, it is possible such deep interaction with an AI might become commonplace, It has already been proposed as as way to integrate humans and computer most successfully.