I was all set to attack the solenoid contacts. Car has been sitting outside freezing for a few days.
20F outside today. Put the voltmeter on the battery, and it only had 3-4V. So had to go get a new battery, and that started it right up.
I was kind of looking forward to taking the solenoid apart, and learning how to do this for myself. Since I also have an 01AvalonXLS and an 07CamryXLE. And a few yrs back, I had my mechanic do the starter problem on this 96camryDX, before I knew anything about Denso contacts.
I kind of like somebody's post about filing the contacts down to the same thickness, and how only the battery side gets worn down.

Rod