So...finally the device is working properly now.
Here's a small report of what I did for those who may be interested.
As I said earlier, the tuner didn't work at all, I just heard static hum from the speakers and couldn't catch any station, so I assumed something was wrong with the tuning voltage and started checking the voltages with my multimeter starting from the entrance to the tuner PCB. Luckily, the problem was diagnosed very fast. As I read here on the forum, the first thing to check here was the TR10 transistor, which was blown, I have changed it with the equivalent modern one.
This had no impact, since the voltages were very high on the emitter, base and collector of TR10, I don't remember exactly, but something around 140V. So, I assumed something was wrong with the Zener diodes close to it. The diode 137 (which is a ZF 9,1V, 1W, BZX55C9V1 Zener diode) was checked with my meter and was defective, so I exchanged it with the equivalent modern one 1N5239.
The problem remained and that's when I found out the completely blown 138 diode (which is a ZF22V Zener diode):
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I have changed this one with the equivalent modern one 1N4748A, 22V, 1W diode.
I turned on the BM4000 and...now I can listen to any FM station I want... finally :)
The device is working properly now with all the bulbs and switches completely in order, I will now refurbish the outer look a little bit and enjoy my NOS Beomaster 4000.
Thanks for reading and thanks to the Beoworld forum for some good advice which helped me!
Here are the faulty items which I changed:
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P.S. does anyone know why the ZF22 diode was screwed (or covered?) to the ground of the metal case? Now everything is working properly, I doubt I should do the same with the new diode...