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How old is the camera? in months or years since you bought it.
Has the camera been dropped or otherwise subjected to mechanical shock(s) in its lifetime?
Has the camera been operated in or subjected to, temperatures below 32 degrees F (freezing point) or above about 100 degrees F ?
Has it ever been subjected to a humidity higher than 85 % or gotten wet ?
Has the camera been operated in a gritty or sandy environment, such as a beach, a seaside, a construction site, or the like?
I would suggest that you try a Factory Reset of the camera. The dial may possibly have been disabled by some obscure setting. A reset of your camera back to factory-issue default settings would show whether this is the case.
(It is true, that a Factory Reset also wipes your camera clean of all custom settings you yourself have programmed into it... though it will not erase date/time settings, not usually, and will never erase pictures taken or videos recorded with the camera and in its storage.)
Do you recall the dial at top right rear of your D3300 ever working, when in Manual Mode, before this? if so, it might also be 'broken'... so that's why I asked the questions about the age, and the excellence of your care, of the camera. So as to judge whether its Nikon Warranty coverage is still valid, or not.
Let me know, please. Thanks.
It's good to hear that you took care of your camera.
But a crucial point, perhaps: is it more than one year old? or less than one year old, measured from date of original purchase?
Try the Factory Settings Reset. It often can cure these problems.