I wrote a bit too fast my message and I skipped some important
information.
When I tried to boot up the computer and noticed it won't do I first
checked the transformer and it showed the right voltage on the voltmeter
screen. I also tried to draw some power using a fixed resistor which
value was chosen to get something around 1 A and indeed the expected
current values flowed within the resistor.
Then when trying to plug back it into the computer I noticed a big spark
everytime I was trying to plug it in. That's when I noticed with an
ohmmeter that the DC input ends were short-circuited. I also tested the
battery, the voltmeter show a nice 0 Volt for each cell while it should
fully charged.
I disassembled the computer and noticed that the short-circuit was caused
by a MOSFET next to the DC input socket on the motherboard but after I
replaced it, this new component also got killed and shorted the DC input
ends.