Thanks for all the help from everyone.
I have cleaned the ignition switch, contacts, and also removed the extra keys on the ignition key ring. Since then, no further problems. The extra weight of the 6 other keys on the ring may have caused a little bouncing around on the bumps. Occasionally, I have turned the ignition switch to the on position, and nothing happened. Back off and then back on, the warning lights and warning beep come on. To me, this indicates an intermittent problem with the switch. I'm going to replace the switch when I get back.
There isn't any visual or obvious problem with the solenoid. All connections are tight and corrosion free. Since it is the original, I'll replace it also.
Terry