Update:
Problem solved. The issue was caused by faulty DC barrel charger. After cutting the cable near the charger and soldering USB-A connector on that end it can be connected to USB charger which supports >= 3A output at 5V. Now the laptop can be charged using DC barrel or USB-C so mainboard is fine, nothing has fried.
Original adapter was giving too high voltage which caused sometimes to start charging and sometimes not. Also when the LED was steady on battery voltage did not raise. Due to too high input voltage on pin OVPSET in chip BQ24171 (above 1.6V which is maximum according to datasheet) what triggered overvoltage protection in that chip. In case someone experiences issues with charging using DC barrel consider buying new good charger (I wouldn't recommend from PINE64).
Problem solved. The issue was caused by faulty DC barrel charger. After cutting the cable near the charger and soldering USB-A connector on that end it can be connected to USB charger which supports >= 3A output at 5V. Now the laptop can be charged using DC barrel or USB-C so mainboard is fine, nothing has fried.
Original adapter was giving too high voltage which caused sometimes to start charging and sometimes not. Also when the LED was steady on battery voltage did not raise. Due to too high input voltage on pin OVPSET in chip BQ24171 (above 1.6V which is maximum according to datasheet) what triggered overvoltage protection in that chip. In case someone experiences issues with charging using DC barrel consider buying new good charger (I wouldn't recommend from PINE64).