4x4 Inner Layers Not Turning

I've had this problem with my 6x6 before, the reason was that some of the internal centers(the ones with screws) were misaligned, causing the cube to lock up. But I don't think this is what's causing your problem unless you've taken it apart and put it back together.
Thanks! That is exactly my problem, I took apart the cube and realigned the centers!
 
good job! 😎

this kind of thing can also often be caused simoly by internal pieces getting out of place (not the centers but the little crescent moon sorta shaped pieces)
usually if you can see them you can either nudge them back in place
or gently pull it out and also one or both edge pieces there and then re-insert the internal piece and reolace the edge pieces
 
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