Check the power supply for burned-out electrolytic capacitors. The power supply board has a two- or three-wire cable going to the power cord connector, possibly through a power filter module. The picture below shows burned-out capacitors with domed-up tops next to some that are good (the tops are flat). I recommend replacing bad capacitors with Panasonic FR-series parts; these have a good combination of power handling ability, longevity and price.
Failing capacitors will work for a while, but as the power quality deteriorates, it gets harder for the set to operate, just as you have observed. It is possible that there is another part with a thermal problem (quits working when it gets warm), but this is the most common failure mode.
An all-seeing tv is the fantasy used in several comedy sketches and dark novels. I have never heard of a tv with an in-built camera but modern spy cameras are small and relatively cheap and even worse easy to buy so it is not beyond the realm of possibilities one could be concealed in a tv - an ideal place as it could provide power so there are no batteries that will need replacing. The lens of such a camera would typically be the size of a match head or even smaller...
Alternatively, I have read how easily some smart security cameras and smart speakers can be hacked.
For any nosy person listening is even easier...
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Without knowing the model or whether you have an instruction manual to follow, the following question on FIXYA from some years ago gave some suggestions. Of course, it is unclear if you have wi-fi or not, or whether you can enter a password using a remote control for your tv. You may want to call your internet provider for assistance.
https://www.fixya.com/support/t25289924-connect_luxor_tv_internet_wireless
About wifi. TV may or may not support your wifi frequency. 2.4 vs 5 ghz. Check your router settings and and reas tv manual. French language channels - there is possibility that those are the only channels available in your area
If you wish to get some details; check the site linked here. Pull up older posts. Surf the site with patience. http://electronicshelponline.blogspot.com/
faults & possible causes to LCD screen are given with illustrations. You can get an idea about the fault to an extent.
The power cable faulty it seems to be a common problem in Luxor TVs if confident unscrew tha back panel the cable is on right hand side of the TV three pinned connection . Release the connector and replace. Or get s TV engineer . He'll repair £10 or £20 . I had same problem six months ago after replacing cable the TV works perfectly