Below is a link to a picture of the lid switch, is located under the speaker cover you should see it popping out the case above the speaker grills, you could try pressing it a few times to get it working.
To rule this out though, remove the speaker cover and unplug the lid switch from the mainboard, if its still the same, you know its not that.
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It could also be a fault with the inverter that these old lcd screens require to power the back light.
If you remove the screen bezel the inverter is the long board below the screen. Its got 2 cables going into it either side. Being carful not to touch the part covered by plastic cover, removed and reinsert both cables and see if it works
Other things to try and reseating the cable at the back of the screen. And remove the speaker cover and reseat the long screen cable to the mainboard.
After reseating these and its still the same id start with replacing the inverter.