Crew was out ... hypoxia ... see details here:
http://en.wikipedia.org/wiki/Helios_Airways_Flight_522
Helios Airways Flight 522 was a scheduled Helios Airways passenger flight that crashed into a mountain on 14 August 2005 at 12:04 pm EEST, north of Marathon and Varnavas, Greece, whilst flying from Larnaca, Cyprus to Athens, Greece.
A lack of oxygen incapacitated the crew, leading to the aircraft’s eventual crash after running out of fuel.
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Takes about 30 seconds w/o oxygen and your reactions are crap at 30,000 feet ... and since your O2 bottle JUST ruptured your hull the ship (and you) are toast (RIP crew and pax).
When Humans Fly High: What Pilots Should Know About High-Altitude Physiology, Hypoxia, and Rapid Decompression
http://www.avweb.com/news/aeromed/181893-1.html?redirected=1
How did they turn off the transponders 20 minutes apart if they were unconscious?
In 20 minutes they would have been dead.
And I got lost on the time line.
How long between the last transmission and the sharp turn to the left?
The auto pilot would have been set up for the route long before they reached 35,000...probably even at the point they set up cruise/climb configuration.
So if the crew was incapacitated, the aircraft would have proceeded to Beijing on its own.
It might have exhausted the fuel before reaching Beijing, depending on how the fuel system on a 777 is designed, but would have tried.