You can test the safety switch (green circle) at this point. Plug the lamp in and while pushing the safety switch all the way down, click through the on settings on the side of the shaft.

If the lamp turns on while your pushing the safety switch in, and turns off when you let go, thats your problem!

You can put the cone back on *properly* so that the switch is pressed down while the cone is on, or use some tape (electrical or duct tape maybe?) to secure the switch down permanently.

If this was not your issue, then you may be able to fix it with the next steps.