(I’m now just going to claim that zero was the extreme I was referring to.)
Edit: The laptop in question — model A31p from 2003 — doesn’t have an accelerometer. http://www.thinkwiki.org/wiki/Category:A31p
Initially, an object falling will accelerate with g=9.81m/s^2, after it reaches the ground it will de-accelerate to a speed of 0m/s in a couple of ms. You are confusing weightlessness/zero-g with no acceleration.
If the drive is falling, certainly it is accelerating toward the ground but the sensor measures zero acceleration. This is the relative frame of reference.