Mindstorms EV3 - Continuous low battery alarm
Update: we made it work, after trying many things, see below.

Opened the brick and inspected it for obvious signs of problems but saw nothing. Even tried with the screen disconnected.

We tried, as suggested in the comment above, with a firmware update. Even though the brick will stay on for only a few seconds, it was enough for the computer to recognize it and see were able to begin the update. It completed without problem, showing that the batteries were ok. After restarting it behaved in the same way. We tried firmware 1.09 and 1.10.

We tried ev3dev, from an SD card. It will also shutdown once it finished booting. But after many tries, it booted and displayed the main ev3dev menu, on which we could see the voltage being 5.10, getting lower gradually until it reached 4.60 and it shutdown.

It seemed obvious it was a hardware issue so we decided to desolder the battery contacts and inspect the board properly. There must be something in the circuit sensing voltage, maybe a resistor going bad and being unable to divide voltage properly. We immediately saw the sign of acid going through the board, with that green/blue colour. We cleaned it with a wire brush, resoldered and it worked! Both the brick's firmware and ev3dev worked perfectly, now seeing 9.10 volts.


I hope this helps someone else with the same problem.
Cheers