CRISIS OVER!!!
Thanks for everyone who has helped me in trying to find the solution... Basically, the problem came from an existing security system that was not taken off properly, hence it causes some interference (apparently) with the new one I just installed. Not really anyone's fault I guess, because the old security system unit was hidden so well.
BUT, I'm very, very glad my Stagea is back to normal!
Now, to the next issue... What should we do with that poor fuel consumption?