Ok for teh sake of TS let me use a idoit proof way of explaining exposure and why you get a black picture.
Think of exposure is a scale from 3 -> infinite where smaller means more light is being let into camera (brighter picture)
Exposure is calculated via shutter + aperature + ISO and each has what we call a stop. To make things simple we make it point system.
So shutter 1/30 is 1 point, 1/60 is 2 point so tat will make 1/4000 7 points
Aperature is the same. 2.8 is 1 point, 4 is 2 point, 5.6 is 3 point, 8 is 4 point and 11 is 5 point
ISO will be 1600 is 1 point, 800 is 2 point, 400 is 3 point, 200 is 4 point and 10 is 5 point
On a bright sunny day, if your exposure is say below 14 points you will get a super over exposed picture. so this is where you can use 1/4000.
1/4000 = 7 point iso100 = 5 point aperature 4 = 2 point
But say indoor, you will need 3 points else it will be dark. So mix and match again
1/30=1 ISO1600=1 Apearture2.8=1
The reason why you getting a black picture is cause you are setting 1/4000 in place that needs 7 point to light up.
1/4000=7 point the rest no matter how u get = not enough light as such you get a super dark picture.
If you still understand simple match above you really should just use auto -.-
Maybe this might help...someone posted this link before.
Now how o take a 1/4000k picture? Simple use a D3 and set ISO 25600 then use the 50 1.4 lens and use 1.4 aperature and here you get it usable 1/4000 indoor =.=
Those insane shutter speeds are not meant to be used in the usual outdoor conditions. If you consider this to be a white elephant then you are perhaps right.