If the module is not functioning (or unplugged for example), the keys will absolutely do nothing. While my keys work, they have abysmal range. Even after replacing batteries. I too suspected the "diversity amplifier" in the top of the tailgate. I even pried it open, and zero corrosion. Sprayed it with electrical cleaner, still nothing.
Need to do the 'ol under the chin trick to unlock the car. Interestingly, using a chinese square diamond, with aftermarket PCB, range returned to normal. I dont have an AK90 or key tool however, to program the chinese diamonds to start the car.

And im still not sure if antenna is actually just faulty, or if the new pcb's on chinese diamonds just have improved range because even a transponder swap on a working OEM PCB resulted in continued poor range.
Disappointed that i cant diagnose this without throwing money into a new amp...