I saw a YouTube video that had this same problem that I was having. It was broken English in the title but no words in the video.
i had no engine codes, no check engine light but the starter would not even attempt to turn over when trying to start.
The diagnosis was the fuel pressure sensor which is located at n the back of the engine. To get to it you have to remove the air cleaner and the intake manifold, and then the aluminum manifold in order to get to the sensor.
Thesensor is $400+ at a lot of websites but on Amazon it was $19.95. You also need a 12 mm crush washer, $7 at Toyota or 10 for $6 on Amazon!
i was sceptical that it would work but for a couple of hours of time and $20, it was worth a shot.
The car started and ran rough for a few seconds, then died...at least the starter was working. Tried again and the engine cranked and with a couple of pumps on the pedal, it caught and is working great. The fuel was drained from the fuel rais and needed to be primed.
So far, so good.
Steve