I finally fixed my ignition!

I removed the whole assembly. Then, I removed the ignition switch from the assembly. Once I did this, it was easy to see there was a problem--there was an aqua-colored plastic disk with a raised portion on one edge under the switch. The raised portion was supposed to keep the valve button pressed in when the key was turned to the last position. It was backwards. I just fooled around with it until it functioned correctly. Man, I'm glad that's fixed.