Thank you for your answer. The laptop seemed totally dead, had lenghty conversation with support and finally got to send it back.
The power adapter seemed to charge the laptop (first orange light, after some time green light) but it did not come to life with the power button.
The return process waws quite complicated since I had paid VAT at the customs and had to declare it again when sending it back so that I can avoid paying VAT again when it ships back…