Hi there, if I google that problem I find a lot of results about that sound happening when trying to start the engine, but in my case it happens when I turn the key just enough to power the system. I can hear the fuel pump for some seconds and the dashboard lights dim a little, then if I try to start the engine everything turns off without any attempt from the starter to start moving.
I identified the noise, it comes from the fuel pump relay since I don't hear the clicking noise nor the pump noise when I pull it off, but the behavior it's the same and if the problem was the relay I think it should still try to start even with a faulty fuel pump relay.

Everything points to a dead battery but the voltage reads 12,7V, which theoretically means it's still good. I won't have a second car to use it's battery to try to start it until tomorrow, so in the meantime maybe you guys have some idea or suggestions about further tests that don't require a second battery?

​

Thanks in advance..

Update: I measured the resistance between the terminals with the key on, without the battery, and it's 33 ohms. Could it be a short-circuit?

Final update: I connected another car's battery to this one through those cables with clamps that come for that purpose and the dashboard and front lights shined at full intensity with no clicking noise but still wouldn't start. But seeing the difference in the lights I thought that maybe the clamps allowed enough contact to power the lights and fuel pump but not enough for the starter, so I went to get a new one with that other car and now it works fine. The question now is how the f**k are those clamps supposed to help if then can at most charge a battery but not start a car from another one in a emergency situation, which is what they're supposedly for.