If you ski is like mine, it's not what you think. The button isn't the issue, it's the lanyard on the DESS post. The next time you have a hard time starting, remove the lanyard from the post and reattach it. Then press the button.
I've had mine apart, and the red rubber cover lays on top of a small microswitch. The microswitch pin is about 1/8" in diameter. Make sure you get the two beeps before you attempt to start.