Weird electrical problem

[manuka]

1997 Avalon - when the outside temperature is about 45 degrees F, when I go to start the car, I turn the key, something goes click, and then the whole car electrical goes dark. I wait a few minutes, various indicator lights come back, and I get to repeat the process again. Sometimes it will work after a few tries. Mostly I have to wait for the temp to get about 10 degrees colder or warmer, and then it's fine. This problem usually only happens in late fall. The rest of the year is fine.

Battery is not discharging, as my aftermarket radio is wired directly to the battery and won't dump its memory each time. Charging and battery have checked out fine on a couple of occasions.

Anyone got any ideas?

[BMR]

Possibly an intermittently bad connection at the battery or a ground cable?

[manuka]

My gut tells me it's something related to the starter, because the electrics don't go dark until the solenoid kicks in. Battery connections and ground appear to be good.