There is no purpose to the logic gates - logic 1 in, logic 1 out, they may as well be replaced by a wire!
The relay should be in the collector circuit and the diode polarity reversed.
Your indiscriminate wiring (and the resultant 'hot resistor') may indicate that you've created more problems than there was originally - to the point of total destruction....
Post lear images of the innards and the points where the wires have been connected.
Same with the lighting controller -...
Aren't those things TTL output? i.e. full of harmonics??? In which case it is entirely UNSUITED to RF application unless you fit a filter on the output.
You won't do yourself any favours by simply obtaining the answer from someone else.
It's not a complicated programming technique - in fact it's one of the basics of serial comms - and you'll benefit enormously from learning how to do it yourself.
The basic description I gave is ample...
Do you have any test equipment (multimeter)?
Browsing the technical manual ( https://www.manualslib.com/manual/1233924/Yamaha-Rx-V675.html#manual ) seems to show the majority of supplies being for digital levels (5V, 3.3V, 1.8V etc) and if any of these have gone 'high' then expect some...
https://www.life360.com/gps-tracking/
If you can find some cheap GPS-enabled mobile phones then you've got yourself a working system.
All you need do is figure out how to charge them.
Of course, vehicle tracking systems are already on the market - as are GSM-enabled trackers.
Find an Arduino sketch that configures for serial data by creating 'clock', 'data' and 'latch' lines. Such configurations are often used for shift-register applications like message board controls (scrolling text displays). Alternatively program three i/o pins yourself and 'bit-bang' the...
Sad to say - this is usually the only option.
If your local authorities are on the ball you can (and should) keep a record of the noise.... times, volume (recordings of it if possible) and even noise levels (there are sound level measuring apps for mobile phones these days). Not sure of your...
Series blocking diodes - suitably rated for current of course - from the charger to each battery will 'isolate' them but you may have to adjust your charger output voltage to compensate for the 0.7V drop they introduce.
Proper supply filtering (local decoupling capacitors etc) and good grounding, supplemented by shielded cables, is as much as even the professional equipment use.
The electronics, including power supplies, should be enclosed as a matter of course.
http://pdf1.alldatasheet.com/datasheet-pdf/view/135651/IRF/IRL640S.html
https://www.digikey.co.uk/products/en?keywords=irl640s
What makes you think it's defective?
You need some form of radio (wireless) comms - be that mobile phone (asssuming there is coverage in that area) or you could develop a system based on the LoRa type transceivers for local (say 25km) coverage (depends on terrain).
But your need to not just detect the item but to send that...
The burning is from 'design' and the spark gaps - typically flashing over when the high voltage used to drive the back light gets excessive (like when the tubes fail....)
Which is also the reason you can see the image but not not when the back light(s) have failed.
It could be the back light...
Depends on its value but certainly anything approaching single figures would be suspect. You should be able to get ESR figures for a 'good' capacitor from the manufacturers data sheet.