Stool height will not adjust at all.

On the top of the cylinder there is a little green button that when pressed, releases the cylinder so it can be adjusted up and down. There is a bolt in the underside of the seat in the adjustment mechanism that is NOT PRESSING THE BUTTON IN so it isn't releasing the cylinder for height adjustment. So...

1. Carefully remove the cylinder from the underside of the seat. When assembled, the cylinder is pressure fit into the adjustment control so it may take some "elbow grease" to remove it from the top.

1.a. Flip the stool upside down and hold the stool off the ground by the cylinder. With a rubber mallet (or a hammer but be sure to protect the metal of the adjustment control) carefully tap around on the underside of the seat. It may take a little time but the top will fall away from the cylinder.

2. Inside the center hole of the adjustment mechanism where the cylinder had been there is a bolt. Turn the bolt COUNTERCLOCKWISE (half a turn at first) to pull the bolt further out of the underside of the seat. This bolt should be out far enough to press the green button when you use the lever to adjust the height, but not so far out that it continually pushes in the green button without using the adjustment lever.

Put the cylinder back into the underside of the seat.  Test and repeat if necessary.