Shine a torch on the display and also try turning it on in a dark room. You should them be able to diagnose if there is simply nothing on the display or the backlight has failed.
If you can take it apart yourself then look at the power supply sor any signs of burnt components or bulging capacitors. If there is nothing obvious then any repair is probably going to consist of changing an entire circuit board at which point it is often uneconomical.
It very nuchal depends on the cause of the failure, and the size and age of the TV, and sometimes the make too.
A few months ago the old fella next door came to see me. His 32" Panasonic was showing the same symptoms: sound, but no picture.
I did the dark room test with a torch. He had no picture but a faint back light. I was able to trace it to a tiny surface-mount fuse no larger than half a grain of rice. The part cost 2p.
That was really lucky. He could easily have had the inverter fail (it powers the backlight) or the X Sus and Y Sus boards. That could have been £60 just for parts.
If it's a decent make and you think it's worth tipping in £100 the track down whoever is local and advertising on Facebook and doing repairs as a little cash-in-hand sideline.
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