This problem started with the first attempt starting the furnace this season. The furnace is rather old.
The pilot light is lit, and it works fine. However, when the heat call comes, the gas starts to flow for an instant, and then the pilot goes out. It is possible that the main burner also briefly (fraction of a second) lights before it all goes out.
The pilot light sensor was changed 3 years ago - it does seem to be sensing and working since the pilot light remains lit, and needs to be heated a bit before it stays on.
I also confirmed that the 24VAC solenoid in the valve is switching (outside of the system). However, I wasn't able to confirm that the valve was open outside the system - as it clearly needs more than just an electrical signal to open the valve. Unfortunately I didn't test it in the system by applying the 24VAC like I did outside. Guess I'll put it back in the system to see.
Ideas?