I had assumed the scenario here is banding in a print, but if we are only talking about monitor view, then yes, depending on the quality of the display and the display profile it is possible to have display banding without corresponding banding in the print. The surest way to check for this is to make a print of an image that looks banded in the display and compare.
Another factor that comes to mind is whether anything you have set-up in the display or in your image processing programs has been changed recently - in the sense that given the equipment you are describing, presumably there was a period of time in which this problem did not happen?