The Trane dealer's technicians came out again today. This time,
luckily, they had a meter hooked up to the new valve when the furnace
failed to ignite. They listened to the sequence of clicks and
discovered that the solenoid didn't "click" when it should have when
the voltage to the solenoid was normal during this period . They
replaced the five day-old valve with another new valve.

I'm keeping my fingers crossed that they have finally solved the
problem.

Thanks to everyone who helped me with this.