But, with the Z axis, there could be one other thing to check.
On my old TP, there were z-locks...two pistons that pointed sideways around the head travel. Initializing the z-motors did not move the z-locks...so, if you were in the maintenance menu, and loading the MOT programs manually, then initializing the Z, the head would bang against the z-lock, and fail. The z-locks had to be manually unlocked before initialization.
Now..the only thing is, I can't recall if there were still z-locks on my MY machine or not. If there are no z-locks, then, it does sound like the z-motor/counter are toast.
There were Z locks on the Midas head area, 2 little solenoids like you mentioned. Previously I had the first error code (F-AXIS-C/9) and after fiddling around, randomly manual unlock the Z locks it came to life, X axis head began to move and it was time for celebration until this error code came up. :(
Anyway after much thinking through and confirming all was well, I believed that the counter could be toast like what you mentioned earlier.
I was thinking if there is possibility that I can just change the counter or the motor itself? The counter on the DC motor on Midas was fixed with its spec details facing inside so I was unable to write down. Perhaps yours maybe facing outwards?
Got posted a picture not sure if it gets through here.