New problems. 2011 Toyota RAV4

Battery died last month. Replaced and then had some idle issues that were fixed with a suggestion in here.

Today I was driving, stopped at a store and when I got back in the car it would not start. No clicks, no trying to turnover, just silence. No dim lights, windows not lagging when I rolled down. Stepdad came to jump it, nothing. Battery voltage was testing normally. Car has newer alternator. One noticable thing though was the coolant was bone dry (engine was not running hot before it died). Oil level good.

I called aaa. Car sat for about an hour and when Aaa pulled up the pos started right away. Drove home, parked, tried to start it again and it was dead again. Let it sit for a few hours and it starts again normally.

Question is where do I start.