My s3 wont boot, not even to the recovery!
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