On page 40 of the user manual, you can find display brightness adjustment mode.
I presume, that the brightness would have been wronged to minimum due to corruption of data. Try to reset the whole system settings. Perhaps the user manual can offer some reset solution.
on the florescent display , at pins 1/2 and 63/64 , there are some 2.2 ohm resistors numbered R 161 and R115 respectively. thaY help filament current . I suspect , one of them is burnt.
perhaps replacing that would restore your display. courtesy Sony, I could get access to service manual