With the camera on try shining a torch at an angle close to the LCD screen and check if you can detect any images at all on the screen, e.g. menus or picture etc.
They will be very faint if they are there so trying this in a darkened room may help.
If you can see images then there is a backlight problem.
Check if the LCD screen’s backlight power flex cable has been securely connected to the motherboard. Here’s an image from the Ifixit Sony α6000 LCD Screen Replacement guide that shows the backlight power cable.
(click on image to enlarge)