@SandyYoung:
It's not really that complicated, it's just a case of applying common sense. The computers are driven by the same sensors that drive the flight deck displays in front of the pilots. If the pilots can see that that their airspeed indications have failed, then it's not a major logical jump to know that the computers have detected that airspeed indication has failed, and it can be reasonably assumed that any protections requiring airspeed information (chief among these being stall protection) will no longer function.
At the risk of sounding like a broken record myself, from this point onwards it doesn't matter if the aircraft you are flying has FBW or conventional controls, glass cockpit or "steam gauges", the onus is on the pilot to diagnose what *is* in fact working and then use that information with their knowledge and training to try to rectify the situation. Sadly, the odds are heavily stacked against even the most experienced and able pilots when they have no outside frame of reference and such a limited time to perform said diagnosis. It's the one situation where the knowledge that one has to do something, coupled with the knowledge that to do the wrong thing could doom you and everyone behind you would put an unbearable amount of mental pressure on even the most unflappable individual or crew.
@Nekkie:
Adrealine is rushing and you see the altimeters showing high rate of descent.
You've also got an attitude indicator telling you you're nose-high. If you see nose-low in your AI and a high rate of descent then you can conclude you're in a dive and pull up. Nose-high with a high rate of descent and the only reasonable conclusion is that you're in a stall and falling. Once you've been able to work that out, you put the nose down and cram on thrust until your stick inputs start to make sense on the AI, you then level out and fly pitch and power until you're confident you're fully in control. The problem, as lots have pointed out, is that it's pitch black outside, so you have no confirmation that your AI is telling you the truth and you've got 3 minutes to make that call with a cacophony of lights, messages and warnings going off around you. Your boss has just entered the cockpit, maybe he can help? But the clock is already ticking...