The key has to be on so the internal valving for the rear DDC shock is open, allowing fluid flow inside the shock which would then allow the shock stroke to be a true value. Picture a needle and seat on a car or bike carburetor. If the key was off, no power to the shock and valve system, that orifice would be closed and the shock wouldn't have the same travel with the rider on board. But it has nothing to do with the adjuster, that is purely mechanical and raises and lowers a collar for spring height, or preload. I'm the guy that had the shop break my DDC preload adjuster. I have a post here somewhere it shows it separated from the shock. There are no electrical connections to the adjuster portion of the rear shock. The wire goes in to the shock on the bottom side. But yes, I think his is broken too. There are 23 full turns lock to lock and it raises and lowers the collar close to 10 mm if I remember. I played with mine before it was installed to count those turns and measure the distance it traveled.
There are used shocks on ebay, buy one of those and rob the adjuster off of it and put it on your bike and you'll be good as before.
Also, in the tool kit I had wondered what that small little plastic 13mm socket is. Turns out it's the special tool to turn the DDC adjuster. If using that and the adjuster hits the stop, but you keep on trying to crank it further, that plastic 13mm special tool socket would break pretty easily at that point. I learned that after the shop broke mine though. I do think it would break on normal use though, since it takes some force to still move that collar up and down it's 10mm of travel.