My s3 wont boot, not even to the recovery! So i have a galaxy s3 and it not rooted or anything, i left it on the chair, came back 15 min later, passed the lock screen the pulled the notifaction bar down and it shut off, it wont turn on with the power button but if i take the battery out and put it back in it boots for a sec and says Samsung then it turns off but sometimes it will get to where it says Galaxy S III and 2 times it gotn to the moving samsung part. Ive tried to go to recovery and it got to the actual recovery 1s but then it said error and shut off
I had that problem with my S3 and it was a faulty power switch that was stuck. My device was rebooting on its own very randomly. 

This video did the trick for me. I found it laughable at first but it worked. Basically, it means that if you tap the device on a flat surface, power button side down, it may release the internal switch.

https://www.youtube.com/watch?v=SSLZFmhmBlc

The guy specifically says in the video "thumbs up if it works, and thumbs down if it doesn't" and it has more thumbs up than down, so... it is a known problem with some S3.

I had to do it 4-5 times in my Galaxy S3's lifetime