There is a good post
here.
To zoom climb to 38k at +7000fpm, at/above their operating ceiling, they were obviously at high power and high speed to start with.
That post explains a way to get to this, with the AP disconnecting once the pitch force got too high. I haven't read or even understood every line by any means but if e.g. you fly level, high power, AP on altitude hold, and you push the stick forward (perhaps because you see IAS=60kt), the pitch trim system will wind the elevator trim backwards, while the autopilot will drive the elevator itself down, with an increasing pitch servo torque, until the pitch servo hits the current limit, and the AP disconnects, leaving you with a severely upwards-trimmed aeroplane which will now shoot upwards, and when it runs out of speed it will stall.
You can do that in my TB20. The yoke push/pull causing the trim wheel to run, is a standard preflight test.
So the three pitot tubes, filled with ice crystals, is what started it all.
What you should get, in any aeroplane, is a TRIM IN MOTION message after about 10 secs of continuous pitch trim movement, but they were probably inundated with error messages.
I can kind of see how it happened, but I don't get why they apparently sat there totally baffled, with so little dialogue or commentary. The 3 of them never realised they were stalled, and (this bit I don't get at all) never realised they were losing altitude at such a fantastic rate. As I said earlier, both the PFD altitude tape and any backup altimeter would have been whizzing round very obviously. -10000 FPM is hard to miss.
One Q is how to recover from such a deep stall. It may be that engine power alone (with full forward yoke/stick) won't do it if the elevator trim is wound all the way back. This came out after the Turkish 737 which crashed at Amsterdam. In that case the only way may be to roll the aircraft onto one side and commence a spiral dive, which will bring the nose down and once you have forward speed, you can level off, trim forward, etc.
