Ok in the manual on page 12 it indicates that there are 5 modes that you can select by pressing the "View Mode" button : you could be on "EVF only +AUTO" and then the LCD screen will not work, you should be on "sensor+EYE SENSOR " . You have to look in the EVF while you toggle the "View Mode" button to see in which mode you are at present.
I have not experienced this with my X-T100 but what I usually do in these situations is do a reset :set-up menu 1 then Set-up reset. Do you have firmware 2.00 installed? But even if it has ver 2.00, reinstall it, then do a reset. If the problem still persist you know its a eye sensor problem. It should still be covered by the 2 year warranty.