Thank you SeanB for making me poke around a little more. The transistors were fine, the relay was fine. Knowing this I watched closer exactly what happens when the relay should click and a saw that the LED went a lot dimmer. This made me think that there is something wrong with the power supply, but the design was different from what I'm used to, so I did not know what components to check. I checked all the capacitors and they were all good, at least their values were good.
Then I started to search online about problems in similar receivers and saw that the X2 capacitors went bad, making all sorts of problems. I checked mine and it was 0,08uF instead of 0,33uF like it should be. I had no ideea that an X2 capacitor could be used in the power supply part because I saw them usually as filters. Anyway, I replaced the X2 capacitor with a 0,47uF one from an old tv board that measures 0,48uF event after about 25 years or more. I also replaced the 100R resistor with 120R one that I had. Now it all works perfectly fine, so this topic is solved and there is no need for the modifications.