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All traces look good... Don't know what to do anymore... I think I will wait for another machine of the same kind arrive here and test the new battery on another computer to see if it burns the battery too...
I measured voltage on burned battery and it measures 12.2V, the same voltage measured on new battery the seller sent me. This is measured not on the connector itself but on the contacts on the battery controller board. Directly on the connector both batteries measure 2.33V
Crappy battery, or not good contact for SYS_DETECT_L line.
Also possible battery processor got blocked for some reason.
I'm sure elements are good, as you have good voltage on them.
But internal processor settled up an error flag, because of short, or overcurrent detected.
In few words only, bad cheap chinese battery...
Well, in the end, as ALWAYS, you were ABSOLUTELY right! I got bad luck and got 3 consecutive bad batteries. The last one the seller sent me is working like a charm now! Thanks for all the help. Mod can close the topic!