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Backlights may go out simply because they have 'burnt out'.
But, sometimes it's either the connection (wiring, connectors) to the power that drives them that is at fault... or, the power supply that goes through that wiring and those connectors, is not being provided. Checking both, by eye and by voltmeter, would be ideal.
Also, without a part # ***** the backlight, it will be difficult to find it. So taking out the defective backlight (if genuinely defective, it's of no use where it is and taking it out won't hurt the device at all, provided you disassemble and reassemble it propery with care etc.), and getting what numbers off it you can - as well as the chance to inspect it and see if it looks defective, broken, or burnt out - would be a good start to the repair process.
The search for a part is always best done with part # ***** part #s in-hand. Let me know what number you get off the backlight, and how it looks, and (if you can) what testing with a voltmeter shows for the wiring and power supplied to the backlight, and I will assist and advise you further.