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If possible, move your eye a little closer to the viewfinder. The viewfinder has a proximity sensor. If you are not close enough to the viewfinder it will not turn on.
This also may happen if the FINDER/LCD Setting option in the menu is set to LCD Monitor. Instead, you may want to change this option to Viewfinder or Auto.
NOTE: If model-specific information is required to complete any of the steps in this solution, refer to the operating instructions supplied with the product.