the aircrew had no external points of reference to fix on, and thus could not orientate themselves as to the correct pitch, yaw or speed of the aircraft.
Bullshit.
Let's assume a complete and total failure of the pitot static system. That takes out 3 instruments: airspeed, altimeter, and vertical speed indicators. Everything else would be fine. Yes, it's true they had no direct measure of the aircraft's speed but they still should have had a working attitude indicator. That would have given them pitch and roll information, and I'm sure there would have been at least some form of skid/slip indication which would have provided yaw information. Engine instruments should have also continued to work normally.
Now, let's talk about how the information they had was enough to keep them alive even in zero visibility. Since their engine instruments were indicating normal performance, and they had pitch and roll information from the attitude indicator, all they needed to do was place the aircraft in a typical climb attitude. This would have resulted in a normal climb, with an airspeed indication that was decidedly not normal.
At this point, it's up to the pilot to decide which of the instruments depicting this impossible situation are wrong. Their situation was also complicated by altimeters that were also not indicating correctly, but the method of resolution should still be the same. Increase throttles to climb power, maneuver the aircraft to a normal climb attitude, then troubleshoot. The pilot's reliance on the least reliable instruments and fixating on them rather than try to use secondary indications of the aircraft's speed (cockpit noise, control surface responsiveness) were what caused that crash. They were in a bad situation, but were in no way "doomed once they took off."
I've personally experienced an airspeed indicator failure while at the controls of a light aircraft at night. Mine was caused by a failure of the instrument itself, but it was still the only direct speed indication in the cockpit. Shortly after takeoff, the airspeed indicator suddenly stopped increasing. I pitched down to accelerate, but saw no change in the gauge. It became clear that it was impossible for me to have pitched down so far and not increased speed, so I checked the other instruments and found I was in a shallow dive and actually losing altitude. I returned the aircraft to what I knew to be a standard climb attitude and returned to the airport without incident. In the beginning, I was far too focused on the failed airspeed indicator, and should have not let things escalate to the point that I was slowly descending at low altitude. I certainly understand how it's tempting to focus in on that and not step back and consider the big picture, but it's what needs to happen in such a situation.