Thanks a lot people for your time and patience and advisesadvice. All of you really tried to help me resolve my problem.
This is incredibly ridiculous, but the problem was not in the cord or adapter or any kind of hardware. I called HP support center to figure what might have gone wrong. It seems like I shut down the laptop before my flight, but what (probably) happened is the laptop didn't shut down correctly, rather went to hibernate mode.
In this case (according to the HP support guy), the laptop won't charge at all (WHAT???) from any sort of cord / wires / chargers. In order to resolve this
the user has to hold the power button on the laptop for 10 seconds.
beforeBefore he/she sees some light flashing on the keyboard then release this power button.
What is this: security feature? Power saving feature? Bug in the software? God knows! And I've been struggling with it several days.
Good thing that I didn't decideddecide to replace the battery, for which in this specific HP model I would have to take the bottom cover out in order to get to the battery. And in our company this is against the policy to dig inside assigned hardware (sealed), which might get us punished even with employee discharge :-)