Being at night and in poor weather they were reliant on their instruments, (as was the flight computer). But rather than standing back and taking stock of the situation they reacted to the first instrument they saw and then panicked. The computer probably told them that summat was out of sorts, and they did the rest, entirely the crews fault, they weren't the first, and they'll probably not be the last
I vaguely recall a similar situation involving a 757 flying at night from Chile to the States. The aircraft had just been washed, and the ground crew had left the pitot tubes covered. The captain failed to notice this on his preflight checks and off they went. It soon became apparent that something wasn't right, with different readings on either side of the cockpit. They contacted ATC, who confirmed that the data in front of the Co pilot was sound. But the flight computer took its information from the Pilots instruments. They couldn't quite understand this, thinking that the computer was right even though the readings didn't match what ATC had told them. They got a bit wrapped up in this, and flew an otherwise servicable and perfectly functioning aircraft into the Pacific. The first warning they had, (because they were distracted and had failed to notice the Copilots altimeter dropping, having discounted it as faulty), was the Ground Radar triggering a Terrain Warning just before they hit the sea

They had options open to them, such as contacting Air Traffic for a true picture of their airspeed, direction and altitude. This would have then given them something to work with. The computer has failsafes which ensure the the pilot always has control, but a bit like the ASR system that Mercedes use, it can be muted, but it will only let you get away with so much. That aircraft would have probably cruised all they way to North Africa/Europe with the controls configured as they were. But as soon as they panicked and pulled the nose up, the computer fought back and tried to level the aircraft, each time it would have lost altitude and we all know what happened next.
That really would have been the flight from hell, every soul on board being awake to the end

The servo assistance of the flight controls is, as Shackeng said, a very considered thing. The joystick is very positive when live, requiring a measured hand, the system that Boeing use is essentially the same, but with a more traditional look and feel to it. If anything the Boeing system feels 'stiffer', but is designed for two handed operation, (although in reality, any well balanced aircraft can be flown with one finger).