@lisbethl according to your images, the backlight does come on. That means your monitor does not receive any video or can't display it. This could be an issue with the LVDS cable but it could also be an issue with the logic board, power circuitry and the T-con board. We would need to know exactly what 820-xxxx your board is.
In the abscences of knowing your logic board version, I would suggest that you measure the voltages on pins 27-29 on the connector at the back of the monitor. Here you should get 12V and on pin 30 you should get 3.3V. All voltages are of course DC. Pin 22-25 on the connector are ground. Careful that you do not shorten the pins out. Let us know what you get.
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