All you people talking about how soft the suspension is, you do realize how little the suspension affects the performance of the woofer, right???
The primary purpose of the suspension (spiders and surround) are to hold the moving assembly in place and keep it from moving non-linearly. The rest of the performance determining factors are dictated 95% by the motor/top plate/ backplate/pole/t-yoke/and moving assembly...
That being said, your suspension looks like the previous owner had something resting on top of the cone, holding it in for an extended period of time. Probably not going to be an easy fix other than a recone.