You may have to check the roots for rot (I'll leave that for others to advise you on).

I just wish to caution you (if you don't already know this) as a Euphorbia, the sap (liquid) this plant exudes CAN BE a skin irritant. Best not to touch your face at all after handling until you've had a chance to wash well. Just so you know.

Too much water,too chilled. AND maybe too dark or all three.

My guess, too dark. Needs more light.

Yes, the soil looks not porous enough, there's not enough light for it, and it's perhaps over-watered and underheated. These ideally want temps above 60F all the time, full sun (or as much light as you can give it), and a soil that doesn't retain a lot of water.

Agree check for root rot ASAP.
It looks like it was kept to cold while wet in a soil that holds to much water.
I wouldn't worry about ideal lighting untill it has shown signs of coming back.

I pulled the three towers out of their soil and y'al were right: packed, moist mess.

So, I cleaned as much of the soil off of hte roots as I could (used a toothbrush even) and have left the towers bare root to dry out. I had read that a euphorbia succulent can survive root bare and out dry for months on end, hope this is true.

I plan on dusting the roots with rooting hormone and then sticking them in a fast draining, porous mix like Al's gritty mix after the roots have thoroughly dried.

It seems like this was a case of overwatering as the tissue of the towers arent mushy and the roots are still white and strong. Will the yellow parts rebound or should I harvest the offshoots and call it a day?

You could always trim back the yellow stems to green growth, and the plant will branch out from there. By the way, I have one of these, 5 feet tall, they grow fast. And when they do outgrow your living space, you can always take cuttings and start over.

Christopher

The yellowed parts looks saveable. Wait before you cut them. If the get worse..glassy,shrunken...then they are done for and then you can make the cut.