I will try to help you with this question.
the fact that the tv still has sound,indicates that this set is up and running ,and the issue will be most likely the unit's backlight inside the LCD panel not working.
Most of the time this is an inverter circuit issue.
This is the circuit that provides the high voltage to power these backlight lamps.
Now,there are a few things that need to be checked first.
please see the flowchart below:
Based on my experience with this model,probably the 24V and the backlight enable voltage will be both all right=the problem will be the inverter circuit.
Now the issue is this inverter circuit is part of the LCD panel.Toshiba does not provide it as a separate assembly.
To replace the whole LCD panel will not be economical since the price of the panel will exceed the cost of a new unit.
Now,this is why Toshiba indicated you to contacted an authorized Toshiba service,because the servicer will sometime be able to get only the inverter from Toshiba,without the whole assy.
The repair estimate to replace only the inverter would be a lot less,maybe around-$200.
But like I said,there is NO part# XXXXX the inverter ,only a Toshiba authorized servicer,at the time when the panel is tried to be authorized prior ordering ,will get eventually a part# XXXXX the inverter board,if toshiba still has it in their stock.
I know,it is frustrating to have a fairly new tv like this failing,but this is the situation now and the best way to approach it is to contact an authorized Toshiba servicer.
I hope this clarifies this matter for you,
Please ,accept my answer only if you are fully satisfied and will be able to leave a positive feedback.
Thank you and have a great day!