After fixing the broken LCD, after I added 2GB of RAM, after re-installing Windowns XP Home from scratch, now the problem with the charging re-appeared.
Now the charging is very moody, sometimes it works, sometimes not.
Initially I thought that this is a connection problem that the charger is not properly plugged in, and sometimes while moving it it was working, and then after 2 sec, it was not working anymore.
It is very strange, because sometimes it charges with no problem I can push the chrager head (plugged in the netbook) in all directions and it still shows as charging.
I opened it 3 times again to check if there is any problem with the electricity socket (connected to the motherboard, where the charger is plugged in), but there is no problem.
The charging light is not turned on at all even when the laptop is switched off. Wihtout the battery but charing it does not work either.
I feel very stupid, because I put a lot of energy into fixing it, and now it does not want to charge. I bought it in 2007, so it has 5 years already, but now with 2GB of RAM and new Windows it woruns smoothley, and I wouldn't want to replace it.