I've checked both ACFET and BATFET in the charging circuit, and they are both fine...
1. So, for now, I've figured out, that SIO and BIOS are OK.
2. Computer boots normally, when both battery and DC plug are connected in specific order. First, I need to plug the DC supply then Battery and computer starts. When turned ON, I see that it draws about 1,4A from the charger, then in the next second, it cuts away ACFET and powers the board from Battery.
3. Charging circuit is charging battery ONLY when the computer is OFF. When the computer is on and I try to reconnect DC power supply, again it charges for a second, then stops.
4. I've checked Power adapter with my Dummy load and it easily provides 6A, voltage drops to around 18,5V, but this is expected due to cable length. And schematic says that VIN is set to >15.2 (AC GOOD), so this cannot be the problem).
I'm going to measure SRN/SRP vs. Iout (it should be 20x SRP-SRN). As discovered I suspect, that there is a problem somewhere in the charging circuit. Thank you all for your suggestions...
I will try to hold tongue at the right angle and hope it helps.