I read a lot about faulty connections and tricks, but non helped, and some were so absurd I did not even try.
Here's what worked for me, and it might for you as well:
- Charge the dead phone for 30 minutes - this is necessary, because the screen may be black and the phone unresponsive, but I noticed that in this state, it will still drain the battery
- Disconnect the phone from the charger
- Now press the ON button really long - I mean really, really long, keep it pressed for way more that a minute.
I can only estimate this, but I reckon after two minutes, my phone booted again.
I have had this situation three times now, something is definitely wrong with my phone, but it is out of warranty and I am glad that so far the above process has always brought it back to life.