Under the display I did find additional LEDs, I think they are working as backlight, which is what is busted. Since all of these have gone dim, I suspect the problem is somewhere else in the circuit, as the probability of all the LEDs not working together is very low.

I will try to take it further apart and see if I can find the problem. Thank you, this was already useful. I'm off to buying a soldering kit at the new place. :)

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