Check the earth wire under the engine mount.
Try a jump lead from engine to a good earth.
Corrosion is a pain.. also worth checking the ring terminals on the starter solenoid.
Also prone to corrosion.
Thanks a lot! I haven't found the earth wire you are talking about. Is it under the car? I can't safely lift it at the moment.
But I have checked with a voltmeter and everything seems to be properly grounded around the engine bay. A few years ago I had a earth problem in the boot, between the battery and the body, but I had solved it and the problem isn't present anymore.
Anyway, you are right, the problem is the corrosion, around the starter solenoid. (More info at the end of my post)
My recommendation would be to inspect the entire circuit. Usually the cables from the alternator to the battery themselves are not the problem. But their connectors can have developed corrosion.
And then there is the return path via ground. Here old cars more often are suffering from issues caused by corrosion. Make sure that the ground cable from the battery is properly connected to the car body. Then, in the engine bay, make sure that the alternator makes properly electrical grounding contact. This is not a separate cable, but the metal housing of the alternator needs to have good contact with the engine and car body.
Thank you for your answer! I've fgound the problem, and in my case it's the wire, not the connector. I admit I'm not sure how the wire cut itself, because it's quite protected and doesn't seem to move much. Also, I'm never driving in the rain, same for the previous owner.
You are right, like I answered to bpirie1000, a few years ago, I had the problem between the battery and the body. I checked again today, but it's still fine!
Same with the alternator, I checked its body was grounded properly to the engine, to the car's body and others earth point.
Have you changed any dash bulbs?
No. And AFAIK, all the dash bulbs are originals. Or at least they have never been changed with LED bulbs. I had read that using LED bulbs in the dashboard, especially for the battery lamp, would cause problems.
So, I found the problem. I started the engine, and the battery was still not charging. Then I moved a bit some random wires, especially those near the starter motor, the alternator and the ECU. And suddenly, the Mini voltmeter started measuring above 13V! And the dashnoard battery lamp switched off.
By checking directly the battery with my voltmeter, it was finally somewhere around 14V! 🤩
Then I moved again the wires a bit, and the voltmeter started showing around 12V, again. After wiggling the wires some more, I found the problem was very close to the solenoid.
At the end, I found the exact wire: it was in a very poor condition, and finally broke on its own (see my attached pics, in red is where the wire is going).
First picture, everything looks alright. Second picture, the wire is completely broken.
The wire was going in a soft tube, then this tube is taped to some corrugated plastic tubes.
This wire is between the "B+" and "D+" wires, in size. So, I'm not sure where it comes from.
Can I just directly add a wire between "B+" of the alternator? Or "D+"? Or something else?
Or does it go through a fuse?
On the wiring diagram for the MPI, there's "hypalon fusible cable", going from the alternator to the starter motor. Is it this cable?
What's the best way for a permanent fix?
Thanks again for all your help!